
Class 
Book 




GoipghtF. 



COECRIGiiT DEPOSIT. 



SCIENTIFIC CULTURE, 



AND OTHER ESSAYS. 



JOSIAH PARSONS COOKE, 

PROFESSOR OF CHEMISTrvY AND MINERALOGY,' IN HARVARD COLLEGE. 



NEW YORK: 
D. APPLETOF AND COMPANY, 

1, 3, and 5 BOND STEEET. 

1881. 




fe 



COPTETGHT BY 

JOSIAII PAESONS COOKE. 

1881. 



TO 

MY ASSOCIATES 

IN 

THE CHEMICAL IABOEATOEY 

OF 

HARVARD COLLEGE 

THIS VOLUME 

IS 

AFFECTIONATELY DEDICATED, 



PREFACE 



The essays collected in this volume, although written 
for special occasions without reference to each other, have 
all a bearing on the subject selected as the title of the 
volume, and are an outcome of a somewhat large experi- 
ence in teaching physical science to college students. 
Thirty years ago, when the writer began his work at 
Cambridge, instruction in the experimental sciences was 
given in our American colleges solely by means of lec- 
tures and recitations. Chemistry and Physics were 
allowed a limited space in the college curriculum as 
branches of useful knowledge, but were regarded as 
wholly subordinate to the classics and mathematics as a 
means of education ; and as physical science was then 
taught, there can be no question that the accepted opin- 
ion was correct. Experimental science can never be 



vi TREFACE. 

made of value as a means of education unless taught by 
its own methods, with the one great aim in view to train 
the faculties of the mind so as to enable the educated 
man to read the Book of Nature for himself. 

Since the period just referred to, the example early 
set at Cambridge of making the student's own ob- 
servations in the laboratory or cabinet the basis of 
all teaching, either in experimental or natural history 
science, has been generally followed. But in most cen- 
ters of education the old traditions so far survive that 
the great end of scientific culture is lost in attempting to 
conform even laboratory instruction to the old academic 
methods of recitations and examinations. These, as 
usually conducted, are simply hindrances in a course of 
scientific training, because they are no tests of the only 
ability or acquirement which science values, and there- 
fore set before the student a false aim. To point out 
this error, and to claim for science teaching its appropri- 
ate methods, was one object of the writer in these essays. 

It is, however, too often the case that, in following 
out our theories of education, we avoid Scylla only to 
encounter Charybdis, and so, in specializing our courses 
of laboratory instruction, there is great danger of falling 



rKEFACE. v ii 

into the mechanical routine of a technical art, and losing 
sight of those grand ideas and generalizations which give 
breadth and dignity to scientific knowledge. That these 
great truths are as important an element of scientific cul- 
ture as experimental skill, the author has also endeavored 
to illustrate, and he has added brief notices of the lives 
of two noble men of science which may add force to the 
illustrations. 



CONTENTS 



PAGE 

I. — Scientific Culture ...... 5 

II. — The Nobility of Knowledge .... 45 

III.— The Elementary Teaching of Physical Science . . 71 

IV. — The Radiometer ...... 86 

V. — Memoir of Thomas Graham . . . . 127 

VI. — Memoir of William IIallowes Miller . . . 145 



ESSAYS 



SCIENTIFIC CULTURE. 

An Address delivered July 7, 1875, at the Opening of the Summer 
Courses of Instruction in Chemistry, at Harvard University, 

You have come together this morning to begin vari- 
ous elementary courses of instruction in chemistry and 
mineralogy. As I have been informed, most of you are 
teachers by profession, and your chief object is to be- 
come acquainted with the experimental methods of teach- 
ing physical science, and to gain the advantages in your 
study which the large apparatus of this university is ca- 
pable of affording. 

In all this I hope you will not be disappointed. You, 
as teachers, know perfectly well that success must de- 
pend, first of all, on your own efforts; but, since the 
methods of studying Nature are so different from those 
with which you are familiar in literary studies, I feel 
that the best service I can render, in this introductory 



6 SCIENTIFIC CULTURE. 

address, is to state, as clearly as I can, the great objects 
which should be Kept in view in the courses on which 
you are now entering. 

By your very attendance on these courses you have 
given the strongest evidence of your appreciation of the 
value of chemical studies as a part of the system of edu- 
cation, and let me say, in the first place, that you have 
not overvalued their importance. The elementary prin- 
ciples and more conspicuous facts of chemistry are so 
intimately associated with the experience of every-day 
life, and find such important applications in the useful 
arts, that no man at the present day can be regarded as 
educated who is ignorant of them. Not to know why 
the fire burns, or how the sulphur trade affects the indus- 
tries of the world, will be regarded, by the generation of 
men among whom your pupils will have to win their 
places in society, as a greater mark of ignorance than a 
false quantity in Latin prosody or a solecism in grammar. 

Moreover, I need not tell you that physical science 
has become a great power in the world. Indeed, after re- 
ligion, it is the greatest power of our modern civilization. 
Consider how much it has accomplished during the last 
century toward increasing the comforts and enlarging the 
intellectual vision of mankind. The railroad, the steam- 
ship, the electric telegraph, photography, gaslights, pe- 
troleum oils, coal-tar colors, chlorine bleaching, anaesthe- 



THE BACONIAN METHOD. 7 

sia, are a few of its recent material gifts to the world ; 
and not only has it made one pair of hands to do the 
work of twenty, but it has so improved and facilitated 
the old industries that what were luxuries to the fathers 
of our republic have become necessities to our genera- 
tion. 

And when, passing from these material fruits, you 
consider the purely intellectual triumphs of physical sci- 
ence, such as those which have been gained with the 
telescope, the microscope, and the spectroscope, you can 
not wonder at the esteem in which these branches of 
study are held in this practical age of the world. 

Now, these immense results have been gained by the 
application to the study of Nature of a method which 
was so admirably described by Lord Bacon in his " No- 
vum Organon," and which is now generally called the 
experimental method. What we observe in Nature is an 
orderly succession of phenomena. The ancients specu- 
lated about these phenomena as well as ourselves, but 
they contented themselves with speculations, animating 
Nature with the products of their wild fancies. Their 
great master, Aristotle, has never been excelled in the 
art of dialectics ; but his method of logic applied to the 
external world was of very necessity an utter failure. It 
is frequently said, in defense of the exclusive study of 
the records of ancient learning, that they are the prod- 



8 SCIENTIFIC CULTURE. 

ucis of thinking, loving, and hating men, like ourselves, 
and it is claimed that the study of science can never rise 
to the same nobility because it deals only with lifeless 
matter. But this is a mere play on words, a repetition 
of the error of the old schoolmen. 

Physical science is noble because it does deal with 
thought, and with the very noblest of all thought. Nat- 
ure at once manifests and conceals an Infinite Presence : 
her methods and orderly successions are the manifesta- 
tions of Omnipotent Will ; her contrivances and laws the 
embodiment of Omniscient Thought. The disciples of 
Aristotle so signally failed simply because they could 
see in Nature only a reflection of their idle fancies. 
The followers of Bacon have so gloriously succeeded 
because they approached Nature as humble students, 
and, having first learned how to question her, have been 
content to be taught and not sought to teach. The an- 
cient logic never relieved a moment of pain, or lifted an 
ounce of the burden of human misery. The modern 
logic has made a very large share of material comfort 
the common heritage of all civilized men. 

In what, then, does this Baconian system consist ? 
Simply in these elements : 1 . Careful observation of the 
conditions under which a given phenomenon occurs ; 2. 
The varying of these conditions by experiments, and ob- 
serving the effects produced by the variation. We thus 



PASTEUR'S EXPERIMENTS. 9 

find that some of the conditions are merely accidental 
circumstances, having no necessary connection with the 
phenomenon, while others are its invariable antecedent. 
Having now discovered the true relations of the phe- 
nomenon we are studying, a happy guess, suggested 
probably by analogy, furnishes us with a clew to the real 
causes on which it depends. We next test our guess by 
further experiments. If our hypothesis is true, this or 
that must follow ; and, if in all points the theory holds, 
we have discovered the law of which we are in search. 
If, however, these necessary inferences are not realized, 
then we must abandon our hypothesis, make another 
guess, and test that in its turn. Let me illustrate by two 
well-known examples : 

The, of old, universally accepted principle that all liv- 
ing organisms are propagated by seeds or germs (omnia 
ex ovo) has been seriously questioned by a modern school 
of naturalists. Yarious observers have maintained that 
there were conditions under which the lower forms of or- 
ganic life were developed independently of all such ac- 
cessories, but other, and equally competent, naturalists, 
who have attempted to investigate the subject, have ob- 
tained conflicting results. 

Thus it was observed that certain low forms of life 
were quite constantly developed in beef juice that had 
been carefully prepared and hermetically sealed in glass 



10 SCIENTIFIC CULTURE. 

flasks, even after these flasks had been exposed for a 
long time to the temperature of boiling water. " Here," 
proclaims the new school, " is unmistakable evidence of 
spontaneous generation; for, if past experience is any 
guide, all germs must have been killed by the boiling 
water." "lo," answer the more cautious naturalists, 
"you have not yet proved your point. You have no 
right to assume that all germs are killed at this tempera- 
ture." 

The experiments, therefore, were repeated under va- 
rious conditions and at different temperatures, but with 
unsatisfactory results, until Pasteur, a distinguished 
French physicist, devised a very simple mode of testing 
the question. He reasoned thus : " If, as is generally 
believed, the presence of invisible spores in the air is 
an essential condition of the development of these low- 
er growths, then their production must bear some pro- 
portion to the abundance of these spores. Near the habi- 
tations of animals and plants, where the spores are known 
to be in abundance, the development would be naturally 
at a maximum, and we should expect that the growth 
would diminish in proportion as the microscope indicated 
that the spores diminished in the atmosphere." 

Accordingly, Pasteur selected a region in the Jura 
Mountains suitable for his purpose, and repeated the well- 
known experiment with beef juice, first at the inn of a 



DAVY'S EXPERIMENTS. 11 

town at the foot of the mountains, and then at various 
elevations up to the bare rocks which covered the top of 
the ridge, a height of some eight thousand feet. At each 
point he sealed up beef juice in a large number of flasks, 
and watched the result. He found that while in the town 
the animalcules were developed in almost all the flasks, 
they appeared only in two or three out of a hundred 
cases where the flasks had been sealed at the top of the 
mountain, and to a proportionate extent in those sealed 
at the intermediate elevations. What, now, did these ex- 
periments prove ? Simply this, that the development of 
these organic forms was in direct proportion to the num- 
ber of germs in the air. It did not settle the question of 
spontaneous generation, but it showed that false conclu- 
sions had been deduced from the experiments which had 
been cited to prove it. 

A still more striking illustration of the same method 
of questioning Nature is to be found in the investigation 
of Sir Humphry Davy, on the composition of water. 
The voltaic battery which works our telegraphs w r as in- 
vented by Yolta in 1800; and later, during the same 
year, it was discovered in London, by Nicholson and Car- 
lisle, that this remarkable instrument had the power of 
decomposing water. These physicists at once recognized 
that the chief products of the action of the battery on 
water were hydrogen and oxygen gases, thus confirming 



12 SCIENTIFIC CULTURE. 

the results of Cavendish, who, in 1781, had obtained wa- 
ter by combining these elementary substances; oxygen 
having been previously discovered in 1775, and hydro- 
gen, at least, as early as 1766. It was, however, very 
soon also observed that there were always formed by the 
action of the battery on water, besides these aeriform 
products, an alkali and an acid, the alkali collecting 
around the negative pole, and the acid around the posi- 
tive pole of the electrical combination. In regard to the 
nature of this acid and alkali, there was the greatest dif- 
ference of opinion among the early experimenters on this 
subject. Cruickshanks supposed that the acid was ni- 
trous acid, and the alkali ammonia. Desormes, a French 
chemist, attempted to prove that the acid was muriatic 
acid ; while Brugnatelli asserted that a new and pe- 
culiar acid was formed, which he called the electric 
acid. 

It was in this state of the question that Sir Humphry 
Davy began his investigation. From the analogies of 
chemical science, as well as from the previous experi- 
ments of Cavendish and Lavoisier, he was persuaded that 
water consisted solely of oxygen and hydrogen gases, and 
that the acid and alkali were merely adventitious prod- 
ucts. This opinion was undoubtedly well founded ; but, 
great disciple of Bacon as he was, Davy felt that his 
opinion was worth nothing unless substantiated by ex- 



DAVY'S EXPERIMENTS. 13 

perimental evidence, and accordingly he set himself to 
work to obtain the required proof. 

In Davy's first experiments the two glass tubes which 
he used to contain the water were connected together by 
an animal membrane, and he found, on immersing the 
poles of his battery in their respective tubes, that, besides 
the now well-known gases, there were really formed muri- 
atic acid in one tube, and a fixed alkali in the other. 
Davy at once, however, suspected that the acid and alkali 
came from common salt contained in the animal mem- 
brane, and he therefore rejected this material and con- 
nected the glass tubes by carefully washed cotton fiber, 
when, on submitting the water as before to the action 
of the voltaic current, and continuing the experiment 
through a great length of time, no muriatic acid ap- 
peared ; but he still found that the water in the one tube 
was strongly alkaline, and in the other strongly acid, al- 
though the acid was chiefly, at least, nitrous acid. A 
part of the acid evidently came from the animal mem- 
brane, but not the whole, and the source of the alkali 
was as obscure as before. 

Davy then made another guess. He knew that alkali 
was used in the manufacture of glass ; and it occurred 
to him that the glass of the tubes, decomposed by the 
electric current, might be the origin of the alkali in 
his experiments. He therefore substituted for the glass 



14 SCIENTIFIC CULTURE. 

tubes cups of agate, which contains no alkali, and re- 
peated the experiment, but still the troublesome acid 
and alkali appeared. Nevertheless, he said, it is pos- 
sible that these products may be derived from some 
impurities existing in the agate cups, or adhering to 
them ; and so, in order to make his experiments as re- 
fined as possible, he rejected the agate vessels and pro- 
cured two conical cups of pure gold, but, on repeating 
the experiments, the acid and alkali again appeared. 

And now let me ask who is there of us who would 
not have concluded at this stage of the inquiry that the 
acid and alkali were essential products of the decompo- 
sition of water ? But not so with Davy. He knew per- 
fectly well that all the circumstances of his experiments 
had not been tested, and until this had been done he had 
no right to draw such a conclusion. He next turned to 
the water he was using. It was distilled water, which he 
supposed to be pure, but still, he said, it is possible that 
the impurities of the spring- water may be carried over 
to a slight extent by the steam in the process of distilla- 
tion, and may therefore exist in my distilled water to a 
sufficient amount to have caused the difficulty. Accord- 
ingly, he evaporated a quart of this water in a silver dish, 
and obtained seven-tenths of a grain of dry residue. He 
then added this residue to the small amount of water 
in the gold cones and again repeated the experiment. 



DAVY'S EXPERIMENTS. 15 

The proportion of alkali and acid was sensibly in- 
creased. 

You think he has found at last the source of the acid 
and alkali in the impurities of the water. So thought 
Davy, but he was too faithful a disciple of Bacon to leave 
this legitimate inference unverified. Accordingly, he re- 
peatedly distilled the water from a silver alembic until it 
left absolutely no residue on evaporation, and then with 
water which he knew to be pure, and contained in vessels 
of gold from which he knew it could acquire no taint, he 
still again repeated the already well-tried experiment. 
He dipped his test-paper into the vessel connected with 
the positive pole, and the water was still decidedly acid. 
He dipped the paper into the vessel connected with the 
negative pole, and the water was still alkaline. 

You might well think that Davy would have been 
discouraged here. But not in the least. The path to the 
great truths which Nature hides often leads through a far 
denser and a more bewildering forest than this ; but then 
there is not infrequently a " blaze " on the trees which 
points out the way, although it may require a sharp eye 
in a clear head to see the marks. And Davy was well 
enough trained to observe a circumstance which showed 
that he was now on the right path and heading straight 
for the goal. 

On examining the alkali formed in this last experi- 



1G .SCIENTIFIC CULTURE. 

ment, lie found that it was not, as before, a fixed alkali, 
soda or potash, but the volatile alkali ammonia. Evi- 
dently the fixed alkali came from the impurities of 
the water, and when, on repeating the experiment with 
pure water in agate cups or glass tubes, the same results 
followed, he felt assured that so much at least had been 
established. There was still, however, the production of 
the volatile alkali and of nitrous acid to be accounted for. 
As these contain only the elements of air and water, 
Davy thought that possibly they might be formed by the 
combination of hydrogen at the one pole and of oxygen 
at the other with the nitrogen of the air, which was nec- 
essarily dissolved in the water. In order, therefore, to 
eliminate the effect of the air, he again repeated the ex- 
periment under the receiver of an air-pump from which 
the atmosphere had been exhausted, but still the acid and 
alkali appeared in the two cups. 

Davy, however, was not discouraged by this, for the 
" blazes " on the trees were becoming more numerous, 
and he now felt sure that he was fast approaching the 
end. He observed that the quantity of acid and alkali 
had been greatly diminished by exhausting the air, and 
this was all that could be expected, for, as Davy knew per- 
fectly well, the best air-pumps do not remove all the air. 
He therefore, for the last experiment, not only exhausted 
the air, but replaced it with pure hydrogen, and then ex- 



EXPERIMENTAL REASONING. 17 

hausted the hydrogen and refilled the receiver with the 
same gas several times in succession, nntil he was per- 
fectly sure that the last traces of air had been as it were 
washed out. In this atmosphere of pure hydrogen he 
allowed the battery to act on the water, and not until the 
end of twenty-four hours did he disconnect the appa- 
ratus. He then dips his test-paper into the water con- 
nected with the positive pole, and there is no trace of 
acid ; he dips it into the water at the negative pole, and 
there is no alkali ; and you may judge with what satis- 
faction he withdraws those slips of test-paper, whose 
unaltered surfaces showed that he had been guided at 
last to the truth, and that his perseverance had been re- 
warded. 

The fame of Sir Humphry Davy rests on his discov- 
ery of the metals of the alkalies and earths which first 
revealed the wonderful truth that the crust of our globe 
consists of metallic cinders ; but none of these brilliant 
results show so great scientific merit or such eminent 
power of investigating Nature as the experiments which 
I have just detailed. I have not, however, described 
them here for the purpose of glorifying that renowned 
man. His honored memory needs no such office at my 
hands. My only object was to show you what is meant 
by the Baconian method of science, and to give some 
idea of the nature of that modern logic which within the 



18 SCIENTIFIC CULTURE. 

last fifty years lias produced more wonderful transfor- 
mations in human society than the author of Aladdin 
ever imagined in his wildest dreams. In this short ad- 
dress I can of course give you but a very dim and im- 
perfect idea of what I have called the Baconian system 
of experimental reasoning. Indeed, you can not form 
any clear conception of it, until in some humble way you 
have attempted to use the method, each one for himself, 
and you have come here in order that you may acquire 
such experience. 

My object, however, will be gained if these illustra- 
tions serve to give emphasis to the following statements, 
which I feel I ought to make at the opening of these 
courses of instruction — statements which have an especial 
appropriateness in this place, since I am addressing teach- 
ers, who are in a position to exert an important influ- 
ence on the system of education in this country. 

In the first place, then, I must declare my conviction 
that no educated man can expect to realize his best possi- 
bilities of usefulness without a practical knowledge of the 
methods of experimental science. If he is to be a physi- 
cian, his whole success will depend on the skill with 
which he can use these great tools of modern civilization. 
If he is to be a lawyer, his advancement will in no small 
measure be determined by the acuteness with which he 
can criticise the manner in which the same tools have 



TRUE AIMS OP STUDY. 19 

been used by his own or bis opponent's clients. If be is 
to be a clergyman, be must take sides in the great con- 
flict between theology and science which is now raging 
in the world, and, unless he wishes to play the part of 
the doughty knight Don Quixote, and think he is win- 
ning great victories by knocking down the imaginary 
adversaries which his ignorance has set up, he must try 
the steel of his adversary's blade. 

Let me be fully understood. It is not to be ex- 
pected or desired that many of our students should 
become professional men of science. The places of 
employment for scientific men are but few, and more 
in the future than in the past they will naturally be 
secured by those whom Nature has endowed with spe- 
cial aptitudes or tastes — usually the signs of aptitudes — 
to investigate her laws. That our country will always 
offer an honorable career to her men of genius, we have 
every reason to expect, and these born students of Nat- 
ure will usually follow the plain indications of Provi- 
dence without encouragement or direction from us. 

It is different, however, with the great body of ear- 
nest students who are conscious of no special aptitudes, 
but who are desirous of doing the best thing to fit them- 
selves for usefulness in the world ; and I feel that any 
system of education is radically defective which does 
not comprise a sufficient training in the methods of ex- 



20 SCIENTIFIC CULTURE. 

perimental science to make the mass of our educated 
men familiar with this tool of modern civilization : so 
that, when, hereafter, new conquests over matter are an- 
nounced and great discoveries are proclaimed, they may 
be able not only to understand but also to criticise the 
methods by which the assumed results have been reached, 
and thus be in a position to distinguish between the true 
and the false. Whether we will or not, we must live un- 
der the direction of this great power of modern society, 
and the only question is whether we will be its ignorant 
slave or its intelligent servant. 

In the second place, it seems fitting that I should 
state to you what I regard as the true aims to be kept in 
view in a course of scientific study, and to give my rea- 
sons for the methods we have adopted in arranging the 
courses you are about beginning. 

In our day there has arisen a warm discussion as to 
the relative claims of two kinds of culture, and attempts 
are made to create an antagonism between them. But 
all culture is the same in spirit. Its object is to awaken 
and strengthen the powers of the mind ; for these, like 
the muscles of the body, are developed and rendered 
strong and active only by exercise ; while, on the other 
hand, they may become atrophied from mere want of use. 
Science culture differs in its methods from the old classi- 
cal culture, but it has the same spirit and the same ob- 



CLASSICAL CULTURE. 21 

ject. Yon must not, therefore, expect me to advocate 
the former at the expense of the latter ; for, although I 
have labored assiduously during a quarter of a century to 
establish the methods of science teaching which have 
now become general, I am far from believing that they 
are the only true modes of obtaining a liberal education. 
So far from this, if it were necessary to choose one of 
two systems, I should favor the classical ; and why ? 

Language is the medium of thought, and can not be 
separated from it. He who would think well must have 
a good command of language, and he who has the best 
command of language I am almost tempted to say will 
think the best. For this reason a certain amount of 
critical study of language is essential for every educated 
man, and such study is not likely to be gained except 
through the great ancient languages ; the advocates of 
classical scholarship frequently say, can not be gained. I 
am not ready to accept this dictum ; but I most willingly 
concede that in the present state of our schools it is not 
likely to be gained. I never had any taste myself for 
classical studies ; but I know that I owe to the study a 
great part of the mental culture which has enabled me 
to do the work that has fallen to my share in life. 

But, while I concede all this, I do not believe, on the 
other hand, that the classical is the only effective method 
of culture ; you evidently do not think so, for you would 



22 SCIENTIFIC CULTURE. 

not be here if you did. But, in abandoning the old tried 
method, which is known to be good, for the new, you 
must be careful that you gain the advantages which the 
new offers ; and you will not gain the new culture you 
seek unless you study science in the right way. In the 
classical departments the methods are so well established, 
and have been so long tested by experience, that there can 
hardly be a wrong way. But in science there is not only 
a wrong way, but this wrong way is so easy and alluring 
that you will most certainly stray into it unless you strive 
earnestly to keep out of it. Hence I am most anxious 
to point out to you the right way, and do what I can to 
keep you in it ; and you will find that our courses and 
methods have been devised with this object. 

When advocating in our mother University of Cam- 
bridge, in Old England, the claims of scientific culture, 
I was pushed with an argument which had very great 
weight with the eminent English scholars present, and 
which you will be surprised to learn was regarded as 
fatal to the success of the science " triposes " then under 
debate. The argument was that the experimental sci- 
ences could not be made the subjects of competitive 
examinations. Some may smile at such an objection ; 
but, as viewed from the English standpoint, there was 
really a great deal in it, and the argument brought out the 
radical difference between scientific and classical culture. 



MENTAL PRIZE-FIGHTS. 23 

The old method of culture may be said to have cuU 
minated in the competitive examinations of the Eng- 
lish universities. We have no such examinations here. 
Success depends not simply on knowing your subject 
thoroughly, but on having it at your fingers' ends, and 
those fingers so agile that they can accomplish not only a 
prodigious amount of work in a short time, but can do 
this work with absolute accuracy. For the only approach 
we make to an experience of this kind, we must look to 
our athletic contests. It may of course be doubted 
whether the ability, once in a man's life, to perform such 
mental feats, is worth what it costs. Still it implies a 
very high degree of mental culture, and it is perfectly 
certain that the experimental sciences give no field for 
that sort of mental prize-fights. It is easy to prepare 
written examinations which will show whether the stu- 
dents have been faithful to their work, but they can not 
be adapted to such competitions as I have described with- 
out abandoning the true object of science culture. The 
ability of the scientific student can only be shown by long- 
continued work at the laboratory table, and by his success 
in investigating the problems which Nature presents. 

We have here struck the true key-note of the scien- 
tific method. The great object of all our study should be 
to study Nature, and all our methods should be directed 
to this one object. This aim alone will ennoble our schol- 



24 SCIENTIFIC CULTURE. 

arsliip as students, and will give dignity to our scientific 
calling as men of science. It is this high aim, moreover, 
which vindicates the worth of the mode of culture we 
have chosen. What is it that ennobles literary culture 
hut the great minds which, through this culture, have 
honored the nations to which they belong ? 

The culture we have chosen is capable of even greater 
things ; not because science is nobler than art, for both 
are equally noble — it is the thought, the conception, which 
ennobles, and I care not whether it be attained through 
one kind of exercise of the mental faculties or another — 
but we are capable of grander and nobler thoughts than 
Plato, Cicero, Shakespeare, or Newton, because we live 
in a later period of the world's history, when, through 
science, the world has become richer in great ideas. It 
is, I repeat, the great thought which ennobles, and it en- 
nobles because it raises to a higher plane that which is 
immortal in our manhood. 

If I have made my meaning clear, and if you sympa- 
thize with my feelings, you will understand why I regard 
culture as so important to the individual and to the na- 
tion. The works of Shakespeare and of Bacon are of 
more value to England to-day than the memories of Blen- 
heim or Trafalgar ; and those great minds will still be 
living powers in the world when Marlborough and Nel- 
son are only remembered as historical names. 



IMPORTANCE OF CULTURE. 25 

I therefore believe that it is the first duty of a coun- 
try to foster the highest culture, and that it should be the 
aim of every scholar to promote this culture both by his 
own efforts and his active influence. A nation can be- 
come really great in no other way. We live in a country 
of great possibilities ; and the danger is that, as with many 
men I have known in college, of great potential abilities, 
the greatness will end where it begins. The scholars of 
the country should have but one voice in this matter, and 
urge upon the government and upon individuals the duty 
of encouraging and supporting mental culture for its own 
sake. 

The time has passed when we can afford to limit the 
work of our higher institutions of learning to teaching 
knowledge already acquired. Henceforth the investi- 
gation of unsolved problems, and the discovery of new 
truth, should be one of the main objects at our American 
universities, and no cost grudged which is required to 
maintain at them the most active minds, in every branch 
of knowledge which the country can be stimulated to 
produce. 

I could urge this on the self-interest of the nation 
as an obvious dictate of political economy. I could 
say, and say truly, that the culture of science will help 
us to develop those latent resources of which we are 
so proud ; will enable us to grow two blades of grass 



26 SCIENTIFIC CULTURE. 

where one grew before ; to extract a larger percentage of 
metal from our ores ; to economize our coal, and in gen- 
eral to direct our waiting energies so that they may pro- 
duce a more abundant pecuniary reward. I could tell of 
Galvani studying for twenty long years, to no apparent 
purpose, the twitching of frogs' hind-legs, and thus sow- 
ing the seed from which has sprung the greatest inven- 
tion of modern times. Or, if our Yankee impatience 
would be unwilling to wait half a century for the fruit 
to ripen, I could point to the purely theoretical investiga- 
tions of organic chemistry, which in less than five years 
have revolutionized one of the great industries of Europe, 
and liberated thousands of acres for a more beneficent 
agriculture. This is all true, and may be urged properly 
if higher considerations will not prevail. It is an argu- 
ment I have used in other places, but I will not use it 
here; although I gladly acknowledge the Providence 
which brings at last even material fruits to reward con- 
scientious labor for the advancement of knowledge and 
the intellectual elevation of mankind. I would rather 
point to that far greater multitude who worked in faith 
for the love of knowledge, and who ennobled themselves 
and ennobled their nation, not because they added to its 
material prosperity, but because they made themselves 
and made their fellows more noble men. 

I come back now again to the moral of all this, to 



CONDITIONS OF CULTURE. 27 

urge upon you, as the noblest patriotism and the most 
enlightened self-interest, the duty of striving for your- 
selves and encouraging in others the highest culture in 
the studies you have chosen, and this culture with one 
end in view, to advance knowledge. I am far, of course, 
from advising you to grapple immaturely with unsolved 
problems, or, when you have gained the knowledge with 
which you can dare to venture from the beaten track, to 
undertake work beyond your power. Many a young 
scientific man has suffered the fate of Icarus in attempt- 
ing to soar too high. Moreover, I am far from expect- 
ing that all or many of you will ever have the opportu- 
nity of going beyond the well-explored fields of knowl- 
edge ; but you can all have the aim, and that aim will 
make your work more worthy and more profitable to 
yourselves. Every American boy can not be President 
of the United States, but if, as our English cousins 
allege, he believes that he can be, the very belief makes 
him an abler man. 

We have dwelt long enough on these generalities, 
and it is time to come down to commonplaces, and to 
inquire what are the essential conditions of this scientific 
culture which shall fit us to investigate Nature ; and the 
first thought that occurs to me in this connection may be 
expressed thus : Science presents to us two aspects, which 
I may call its objective and its subjective aspect. Objec- 



28 SCIENTIFIC CULTURE. 

lively it is a body of facts, which we have to observe 
and subjectively it is a body of truths, conclusions, or in- 
ferences, deduced from these facts ; and the two sides of 
the subject should always be kept in view. 

I propose next to say a few words in regard to each of 
these two aspects of our study, and in regard to the best 
means of training our faculties so as to work successfully 
in each sphere. First, then, success in the observation of 
phenomena implies three qualities at least, namely, quick- 
ness and sharpness of perception, accuracy in details, and 
truthfulness ; and on its power to cultivate these quali- 
ties a large part of the value of science, as a means of 
education, depends. 

To begin with the cultivation of our perceptions. 
We are all gifted with senses, but how few of us use 
them to the best advantage ! " We have eyes and see 
not " ; for, although the light paints the picture on the 
retina, our dull perceptions give no attention to the 
details, and we retain only a confused impression of 
what has passed before our eyes. " But how," you may 
ask, " are we to cultivate this sharpness of perception ? " 
I answer, only by making a conscious effort to fix our 
attention on the objects we study until the habit be- 
comes a second nature. I have often noticed, with sur- 
prise, the power which uneducated miners frequently 
possess of recognizing many minerals at sight. This 



POWER OF OBSERVATION. 29 

they have acquired by long experience and close famili- 
arity with such objects, and such power of observation 
is with them so purely a habit that they are frequently 
unable to state clearly the grounds on which their con- 
clusions are based. They recognize the minerals by what 
in common language is called their " looks " and they 
notice delicate differences in the " looks " to which most 
men are blind. It is, however, the business of the scien- 
tific mineralogist to analyze these " looks," and to point 
out in what the differences consist ; so that by fixing his 
attention on these points the student may gain, by a few 
hours' study, the power which the miner acquires only 
after long experience. 

The chief difficulty, however, which we find in teach- 
ing mineralogy is, that the students do not readily see 
the differences when they are pointed out, or, if they 
see them, do not remember them with sufficient pre- 
cision to render their subsequent observations conclu- 
sive and precise. This either arises from a failure to 
cultivate the powers of observation in childhood, or the 
subsequent blunting of them by disuse. The ladies 
will scout the idea that a brooch of cut-glass is as orna- 
mental as one of diamond, and yet I venture to assert 
that there is not one person in fifty, at least of those 
who have not made a study of the subject, who can 
tell the difference between the two. The external ap- 



30 SCIENTIFIC CULTURE. 

pearance depends simply on what we call lustre. The 
lustre of glass is vitreous, that of the diamond adaman- 
tine ; and I know of no other distinction which it is more 
difficult for students to recognize than this. Those of 
you who study mineralogy will experience this difficulty, 
and it can be overcome only by giving careful attention 
to the subject. The teacher can do nothing more than 
put in your hands the specimens which illustrate the 
point, and you must study these specimens until you see 
the difference. It is a question of sight, not of under- 
standing, and all the optical theories of the cause of the 
lustre will not help you in the least toward seeing the 
difference between diamond and glass, or anglesite and 
heavy spar. 

Another illustration of the same fact is the constant 
failure of students to distinguish by the eye alone be- 
tween the two minerals called copper-glance and gray 
copper. There is a difference of color and lustre which, 
although usually well marked, it requires an educated 
eye to distinguish. 

Mineralogy undoubtedly demands a more careful cul- 
tivation of the perceptions than the other branches of 
chemistry ; but still you will find abundant practice for 
close observation in them all. I have often known stu- 
dents to reach erroneous results in qualitative analysis by 
mistaking a white precipitate in a colored liquid for a 



ACCURACY IN DETAILS. 31 

colored precipitate, or by not attending to similar broad 
distinctions, which would have been obvious to any care- 
ful observer ; and so in quantitative analysis, mere deli- 
cacy of touch or handling is a great element of success. 

But I must pass on to speak of the importance in the 
study of Nature of accuracy in detail, which is the sec- 
ond condition of successful observation of which I spoke. 
"We must cultivate not only accuracy in observing details, 
but also accuracy in following details which have been 
laid down by others for our guidance. In science we 
can not draw correct conclusions from our premises un- 
less we are sure that we have all the facts, and what 
seemed at first an unimportant detail often proves to be 
the determining condition of the result; and, again, if 
we are told that under certain conditions a certain sign is 
the proof of the presence of a certain substance, we have 
no right to assume that the sign is of any value unless 
the conditions are fulfilled. A black precipitate, for ex- 
ample, obtained under certain conditions, is a proof of 
the presence of nickel, but we can not assert that we 
have found nickel unless we have followed out those 
details in every particular. 

Of course, we must avoid empiricism as far as we 
can. We must seek to learn the reasons of the details, 
and such knowledge will not only render our work in- 
telligent, but will also frequently enable us to judge 



32 SCIENTIFIC CULTURE. 

how far the details are essential, and to what extent 
our processes may be varied with safety. We must also 
avoid trifling, and, above all, "the straining at a gnat 
and swallowing a camel," as is the habit with triflers. 
Large knowledge and good judgment will avoid all such 
errors ; but, if we must choose between f ussiness and 
carelessness, the first is the least evil. Slovenly work 
means slovenly results, and habits of carefulness, neat- 
ness, and order produce as excellent fruits in the labora- 
tory as in the home. 

Last in order but first in importance of the conditions 
of successful observation, mentioned above, stands truth- 
fulness. Here you may think I am approaching a deli- 
cate subject, of which even to speak might seem to cast 
a reproach. But not so at all. I am not speaking here 
of conscious deception, for I assume that no one who as- 
pires to be a student of Nature can be guilty of that. 
But I am speaking of a quality whose absence is not 
necessarily a mark of sinfulness, but whose possession, in 
a high degree, is a characteristic of the greatest scien- 
tific talent. As every lawyer knows, he is a rare man 
whose testimony is not colored by his interests, and a 
very large amount of self-deception is compatible with 
conscious honesty of purpose. 

So among scientific students the power to keep the 
mind unbiased, and not to color our observations in the 



TRUTHFULNESS IN WORK. 33 

least degree, is one of the rarest as it is one of the 
noblest of qualities. It is a quality we must strive 
after with all our might, and we shall not attain it un- 
less we strive. Remember, our observations are our 
data, and, unless accurate, everything deduced from them 
must have the taint of our deception. "We can not de- 
ceive Nature, however much we may deceive ourselves ; 
and there is many a student who would cut off his right 
hand rather than be guilty of a conscious untruth, who 
is yet constantly untruthful to himself. Every year stu- 
dents of mineralogy present to me written descriptions 
of mineral specimens which particularize, as observed, 
characters that do not appear on the specimen given them 
to determine, although they may be the correct charac- 
ters of some other mineral. 

There is usually no want of honesty in this, but, de- 
ceived by some accident, the student has made a wrong 
guess, and then imagined that he saw on the specimen 
those characters which he knew from the descriptions 
ought to appear on the assumed mineral. So, also, it not 
un frequently happens that a student in qualitative analy- 
sis, who has obtained some hints in regard to the composi- 
tion of his solution, will torture his observations until they 
seem to him to confirm his erroneous inferences; and 
again the student in quantitative analysis, who finds out 
the exact weight he ought to obtain, is often insensibly 



34 SCIENTIFIC CULTURE. 

influenced by this knowledge — in the washing and igni- 
tion of his precipitate, or in some other way — and thus 
obtains results whose only apparent fault may be a too 
close agreement with theory, but which, nevertheless, 
are not accurate because not true. It is evident how 
fatal such faults as these must be to the investigation of 
truth, and they are equally destructive of all scientific 
scholarship. Their effect on the student is so marked 
that, although he may deceive himself, he will rarely de- 
ceive his teacher. That he should lose confidence in his 
own results is, to the teacher, one of the most marked 
indications of such false methods of studv, but the stu- 
dent usually refers his want of success to any cause but 
the real one — his own untruthfulness. He will complain 
of the teacher, or of the methods of instruction, and may 
even persuade himself that all scientific results are as un- 
certain as his own. As I have said, mere ordinary truth- 
fulness, which spurns any conscious deception, will not 
save us from falling into such faults. Our scientific 
study demands a much higher order of truthfulness than 
this. We should so love the truth above all price as to 
strive for it with single-hearted and unswerving purpose. 
We must be constantly on our guard to avoid any cir- 
cumstance which would tend to bias our minds or warp 
our judgments, and we must make the attainment of 
the truth our sole motive, guide, and end. 



SUBJECTIVE ASPECT OF STUDY. 35 

It remains for me, before closing this address, to say 
a few words on what I have called the subjective aspect 
of scientific study. Science offers us not only a mass of 
phenomena to be observed, but also a body of truths 
which have been deduced from these observations ; and, 
without the power of drawing correct inferences from 
the data acquired, exact observations would be of little 
value. I have already described the inductive method of 
reasoning, and illustrated it by two noteworthy examples, 
and, in a humbler measure, we must apply the same 
method in our daily work in the laboratory. We must 
learn how to vary our experiments so as to eliminate the 
accidental circumstances, and make evident the essential 
conditions of the phenomena we are studying. Such 
power can only be acquired by practice, and a somewhat 
long experience in active teaching has convinced me that 
there is no better means of training this logical faculty 
than the study of qualitative chemical analysis in which 
many of you are to engage. 

The results of the processes of qualitative analysis 
are perfectly definite and trustworthy ; but they are only 
reached by following out the indications of experiments 
which are frequently obscure, and even apparently con- 
tradictory; reconciling by new experiments the seem- 
ing discrepancies, and, at last, having eliminated all 
other possible causes of the phenomena observed, dis- 



36 SCIENTIFIC CULTURE. 

covering the true nature of the substances under exami- 
nation. 

The study of mineralogy affords an almost equally 
good practice, although in a somewhat different form. 
By comparing carefully many specimens of the same 
mineral, you learn to distinguish the accidental from the 
essential characters, and on this distinction you must 
base your inferences in regard to the nature of the speci- 
mens you may be called upon to determine. A single 
remark occurs to me which may aid you in cultivating 
this scientific logic. 

Do not attempt to reason on insufficient data. Multi- 
ply your observations or experiments, and when your pre- 
mises are ample, the conclusion will generally take care 
of itself. Are you in doubt in regard to a mineral speci- 
men? Repeat your observations again and again, multi- 
ply them with the aid of the blow-pipe or goniometer, 
compare the specimen with known specimens which it 
resembles, until either your doubts are removed or you 
are satisfied that you are unequal to the task ; and remem- 
ber that, in many cases, the last is the only honest conclu- 
sion. 

Are you in doubt in regard to the reactions of the 
substance you are analyzing, whether they are really those 
of a metal you suspect to be present % Do not rest in 
such a frame of mind, and, above all, do not try to re- 



REASONING FACULTIES. 37 

move the doubt by comparing your experience with that 
of your neighbor, but multiply your own experiments ; 
procure some compound of the metal, and compare its 
reactions with those you have observed until you reach 
either a positive or a negative result. 

Eemember that the way to remove your doubts is 
to widen your own knowledge, and not to depend on 
the knowledge of others. When your knowledge of the 
facts is ample, your inferences will be satisfactory, and 
then an unexplained phenomenon is the guide to a new 
discovery. Do not be discouraged if you have to labor 
long in the dark before the day begins to dawn. It will 
at last dawn to you, as it has dawned to others before, 
and, when the morning breaks, you will be satisfied with 
the result of your labor. 

Moreover, I feel confident that such experience will 
very greatly tend to increase your appreciation of the 
value of scientific studies in training the reasoning facul- 
ties of the mind. This, as every one must admit, is the 
best test of their utility in a scheme of education, and it 
is precisely here that I claim for them the very highest 
place. It has generally been admitted that mathemati- 
cal studies are peculiarly well adapted to train the logi- 
cal faculties, but still many persons have maintained that, 
since the mathematics deal wholly with absolute certain- 
ties, an exclusive devotion to this class of subjects unfits 



38 SCIENTIFIC CULTURE. 

the mind for weighing the probable evidence by which 
men are chiefly guided in the affairs of life. 

But, without attempting to discuss this question, on 
which much might be said on both sides, it is certain that 
no such objection can be urged against the study of the 
physical sciences if conducted in the manner I have at- 
tempted to describe. These subjects present to the con- 
sideration of the student every degree of probable evi- 
dence, accustoming him to weigh all the evidence for or 
against a given conclusion, and to reject or to provision- 
ally accept only on the balance of probabilities. More- 
over, in practical science, the student is taught to fol- 
low out a chain of probable evidence with care and cau- 
tion, to eliminate all accidental phenomena, and supply, 
by experiment or observation, the missing links, until 
he reaches the final conclusion — an intellectual process 
which, though based wholly on probable evidence, may 
have all the force and certainty of a mathematical demon- 
stration. 

Indeed, that highly valued scientific acumen and skill 
which enables the student to brush away the accidental 
circumstances by which the laws of Nature are always 
concealed until the truth stands out in bold relief, is 
but a higher phase of the same talent which marks 
professional skill in all the higher walks of life. The 
physician who looks through the external symptoms of 



BEAUTY OF NATURE 39 

his patient to the real disease which lurks beneath ; 
the lawyer, who disentangles a mass of conflicting testi- 
mony, and follows out the truth successfully to the end ; 
the statesman, who sees beneath the froth of political life 
the great fundamental principles which will inevitably 5 
rule the conduct of the state, and thus foresees and pro- 
vides for the coming change ; the general, who discovers 
amid the confusion of the battlefield the weak point of 
his enemy's front ; the merchant, even, who can inter- 
pret the signs of the unsettled market — employ the same 
faculty, and frequently in not a much lower degree, that 
discovered the law of gravitation, and which, since the 
days of Newton, has worked so successfully to unveil the 
mysteries of the material creation. 

Moreover, I hope, my friends, that you will come to 
value scientific studies, not simply because they cultivate 
the perceptive and reasoning faculties, but also because 
they fill the mind with lofty ideals, elevated conceptions, 
and noble thoughts. Indeed, I claim that there is no 
better school in which to train the sesthetical faculties of 
the mind, the tastes, and the imagination, than the study 
of natural science. 

The beauty of Nature is infinite, and the more we 
study her works the more her loveliness unfolds. The 
upheaved mountain, with its mantle of eternal snow ; the 
majestic cataract, with its whirl and roar of waters ; 



40 SCIENTIFIC CULTURE. 

the sunset cloud, with its blending of gorgeous hues, 
lose nothing of their beauty for him who knows the mys- 
tery they conceal. On the contrary, they become, one 
and all, irradiated by the Infinite Presence which shines 
through them, and fill the mind with grander conceptions 
and nobler ideas than your uneducated child of Nature 
could ever attain. 

Remember that I am not recommending an exclu- 
sive devotion to the natural sciences. I am only claim- 
ing for them their proper place in the scheme of edu- 
cation, and I do not, of course, deny the unquestionable 
value of both the ancient and the modern classics in 
cultivating a pure and elevated taste. But I do say 
that the poet-laureate of England has drawn a deeper 
inspiration from Nature interpreted by science than any 
of his predecessors of the classical school ; and I do 
also affirm that the pre-Raphaelite school of painting, 
with all its grotesque mimicry of Nature, embodies a 
truer and purer ideal than that of any Eoman fable or 
Grecian dream. 

And what shall we say of the imagination ? "Where 
can you find a wider field for its exercise than that 
opened by the discoveries of modern science ? And as 
the mind wanders over the vast expanse, crossing bound- 
less spaces, dwelling in illimitable time, witnessing the 
displays of immeasurable power, and studying the adapta- 



MEMORIZING. 41 

tions of Omniscient skill, it lives in a realm of beauty, 
of wonder, and of awe, such as no artist has ever at- 
tained to in word, in sound, in color, or in form. And 
if suck a life does not lead man to feel kis own depend- 
ence, to yearn toward tke Infinite Fatker, and to rest 
on tke bosom of Infinite Love, it is simply because it 
is not tke noble in intellect, not tke great in talent, not 
tke profound in knowledge, not tke rick in experience, 
not tke lofty in aspiration, not tke gifted in imagery, 
but solely tke pure in keart, wko see God. 

Suck, tken, is a very imperfect presentation of wkat 
I believe to be tke value of scientific studies as a means 
of education. In wkat I kave stated I kave implied tkat, 
for tkese studies to be of any real value, tke end must be 
constantly kept in view, and everytking made subservi- 
ent to tke one great object. 

To study tke natural sciences merely as a collec- 
tion of interesting facts wkick it is well for every edu- 
cated man to know, seldom serves a useful purpose. Tke 
young mind becomes wearied witk tke details, and soon 
forgets wkat it kas never more tkan kalf acquired. Tke 
lessons become an exercise of tke memory and of notking 
more ; and if, as is too frequently tke case, an attempt 
is made to cram tke kalf-formed mind in a single sckool- 
year witk an epitome of kalf tke natural sciences — natu- 
ral pkilosopky, astronomy, and ckemistry, pkysiology, 



42 SCIENTIFIC CULTURE. 

zoology, botany, and mineralogy, following each, other 
in rapid succession — these studies become a great evil, 
an actual nuisance, which I should be the first to vote 
to abate. The tone of mind is not only not improved, 
but seriously impaired, and the best product is a super- 
ficial, smattering smartness, which is the crying evil not 
only of our schools but also of our country. 

In order that the sciences should be of value in our 
educational system, they must be taught more from 
things than from books, and never from books with- 
out the things. They must be taught, also, by real liv- 
ing teachers, who are themselves interested in what they 
teach, are interested also in their pupils, and under- 
stand how to direct them aright. Above all, the teach 
ers must see to it that their pupils study with the under- 
standing, and not solely with the memory, not permit- 
ting a single lesson to be recited which is not thoroughly 
understood, taking the greatest care not to load the mem- 
ory with any useless lumber, and eschewing merely mem- 
orized rules as they would deadly poison. The great 
difficulty against which the teachers of natural science 
have to contend in the colleges are the wretched tread- 
mill habits the students bring with them from the schools. 
Allow our students to memorize their lessons, and they 
will appear respectably well, but you might as easily re- 
move a mountain as to make many of them think. They 



EARLY PREPARATION. 43 

will solve an involved equation of algebra readily enough 
so long as they can do it by turning their mental crank, 
when they will break down on the simplest practical 
problem of arithmetic which requires of them only 
thought enough to decide whether they shall multiply or 
divide. 

Many a boy of good capabilities has been irretriev- 
ably ruined, as a scholar, by being compelled to learn 
the Latin grammar by rote at an age when he was in- 
capable of understanding it; and I fear that schools 
may still be found where young minds are tortured by 
this stupefying exercise. Those of us who have faith 
in the educational value of scientific studies are most 
anxious that the students who resort to our colleges 
should be as well fitted in the physical sciences as in the 
classics, for otherwise the best results of scientific culture 
can not be expected. As it is, our students come to the 
university, not only with no preparation in physical sci- 
ence, but with their perceptive and reasoning faculties so 
undeveloped that the acquisition of the elementary prin- 
ciples of science is burdensome and distasteful ; and good 
scholars, who are ambitious of distinction, can more 
readily win their laurels on the old familiar track than 
on an untried course of which they know nothing, and 
for which they must begin their training anew. 

We have improved our system of instruction in the 
4 



44: SCIENTIFIC CULTUKE. 

college as fast as we could obtain the means, but we are 
persuaded that the best results can not be reached without 
the cooperation of the schools. We feel, therefore, that it 
is incumbent upon us, in the first place, to do everything 
in our power to prove to the teachers of this country how 
great is the educational value of the physical sciences, 
when properly taught ; and secondly, to aid them in ac- 
quiring the best methods of teaching these subjects. It 
is with such aims that our summer courses have been in- 
stituted, and your presence here in such numbers is the 
best evidence that they have met a real want of the com- 
munity. "We welcome you to the university and to such 
advantages as it can afford, and we shall do all in our 
power to render your brief residence here fruitful, both 
in experience and in knowledge ; hoping, also, that the 
university may become to you, as she has to so many 
others, a bright light shining calmly over the troubled 
sea of active life, ever suggesting lofty thoughts, encour- 
aging noble endeavors, and inciting all her children to 
work together toward those great ends, the advancement 
of knowledge and the education of mankind. 



n. 
THE NOBILITY OF KNOWLEDGE. 

An Address delivered before the Free Institute at Worcester, Massa- 
chusetts, July 28, 181 '4. 

Within a comparatively few years schools for the 
instruction of artisans have become a prominent feature 
in the educational systems both of this country and of 
Europe, and seem destined to supersede the old system of 
apprenticeships. The establishment of these schools has 
been an important step in human progress, not because 
any great advantage has been gained in the cultivation of 
mechanical skill, but because here the future mechanic 
acquires culture of the mind as well as skill of the hand. 
Indeed, it may be doubted whether our utilitarian age can 
ever successfully compete with those "elder days of art" 
when 

"Builders wrought with greatest care 
Each minute and unseen part." 



46 THE NOBILITY OF KNOWLEDGE. 

But, if our industrial schools do not make better me- 
chanics than the workshops of the olden time, they cer- 
tainly educate better men, and, by adding to skill, knowl- 
edge, they are elevating the mechanic and ennobling his 
calling. 

If, therefore, these schools are the representatives in 
our age of the workshops with their bands of apprentices 
in the days of yore, then that by which the schools are 
distinguished, that which they have added to the old 
system, is not art but mental culture ; and therefore, when 
asked to address you on this occasion, I could think of no 
more appropriate subject than the Nobility of Knowledge. 

Identified with an institution in which mental culture 
is the chief aim, I felt that I was asked to address a body 
of cultivated working-men with whom, though employed 
in the mechanic arts, the acquisition of knowledge was 
also a privilege and a pride. I felt, moreover, that a 
proper appreciation of the true dignity of knowledge, in 
itself considered, and apart from all economical consid- 
erations, is one of the great wants of our age and of our 
country. 

"Knowledge is power." "Knowledge is wealth." 
These trite maxims are sufficiently esteemed in our com- 
munity, and need not that they be enforced by any one. 
So far as knowledge will yield immediate distinction or 
gain, it is sought and fostered by multitudes. But, when 



MATERIAL ADVANTAGES. 47 

the aim is low, the attainment is low, and too many of 
our students are satisfied with superficiality, if it only glit- 
ters, and with charlatanry, if it only brings gold. 

Let me not be understood to depreciate the material 
advantages of learning. I rejoice that in this world 
knowledge frequently yields wealth and fame, and I 
should have little hope for human progress were the 
prizes of scholarship less than they are. Power and 
wealth are noble aims, and when rightly used may be 
the means of conferring unmeasured blessings on man- 
kind ; but I desire at this time to impress upon you, my 
friends, the fact that knowledge has nobler fruits than 
these, and that the worth of your knowledge is to be 
measured not by the credits it will add to your account 
in the ledger, or the position it may give you among 
men, but by the extent to which it educates your higher 
nature, and elevates you in the scale of manhood. 

I address young men who are just entering on life, 
who are at an age when the mystery of our being usually 
presses most closely upon the soul, and whose aspirations 
for higher culture and clearer vision have not been dead- 
ened by the sordid damps of the world. Trust no croak- 
ers who tell you that your youthful visions are illusions, 
which a little contact with the real business of the world 
will dispel. 

It is only too true that these visions will become 



48 THE NOBILITY OF KNOWLEDGE. 

fainter and fainter, if you allow the cares of the world 
to engross your thoughts ; but, unless your higher nat- 
ure becomes wholly deadened, you will look back to the 
time when the visions were brightest, as the golden pe- 
riod of your life, and let me assure you that, if you only ' 
are true to the aspirations of your youth, the visions will 
become clearer and clearer to the last, and, as we firmly 
believe, will prove to be the dawn of the perfect day. 

My friends, if you have seen these visions, " the no- 
bility of knowledge " has been a reality of your experi- 
ence. You know that there is a life lived in communion 
with the thoughts of great men or with the thoughts of 
God as we can read them in Nature and Eevelation, 
which is purer and nobler than a life of money-making 
or political intrigue, and I would that I could so bring 
you to appreciate not only the nobility, but also the 
happiness, of such a life as to induce you to try to 
live it. 

Do you tell me that it is only granted to a few men 
to become scholars, and that you have been educated 
for some industrial pursuit? Remember, as I said be- 
fore, that it is your special privilege to have been edu- 
cated, to have added knowledge to your handicraft, and 
that this very knowledge, if kept alive so far as you are 
able, will ennoble your life. Knowledge, like the fairy's 
wand, ennobles whatever it touches. The humblest occu- 



VALUE OF UNIVERSITIES. 49 

pations are adorned by it, and without it the most exalted 
positions appear to true men mean and low. 

JSTor is it the extent of the knowledge alone which 
ennobles, but much more the spirit and aim with which 
it is cultivated, and that spirit and aim you may carry 
into any occupation, however engrossing, and into any 
condition of life, however obscure. 

And let me add that what I have said is true not only 
of the individual, but also, and to an even greater degree, 
of the nation. Our people, for the most part, look upon 
universities and other higher institutions of learning as 
merely schools for recruiting the learned professions, and 
estimate their efficiency solely by the amount of teaching 
work which they perform. But, however important the 
teaching function of the university may be, I need not 
tell you that this is not its only or chief value to a com- 
munity. The university should be the center of scientif- 
ic investigation and literary culture, the nursery of lofty 
aspirations and noble thoughts, and thus should become 
the soul of the higher life of the nation. For this and 
this chiefly it should be sustained and honored, and no 
cost and no sacrifice can be too great which are required 
to maintain its efficiency ; and its success should be meas- 
ured by the amount of knowledge it produces rather 
than by the amount of instruction it imparts. 

Harvard College^ by cherishing and honoring the 



50 THE NOBILITY OF KNOWLEDGE. 

great naturalist she has recently lost, has done more for 
Massachusetts than by educating hosts of commonplace 
professional men. The simple title of teacher, which in 
his last will Louis Agassiz wrote after his name, was a 
nobler distinction than any earthly authority could con- 
fer; but remember he was a teacher not of boys, but of 
men, and his influence depended not on the instruction in 
natural history which he gave in his lecture-room, but on 
his great discoveries, his far-reaching generalization, and 
his noble thoughts. Although that man died poor, as the 
world counts poverty, yet the bequest which he left to 
this people can not be estimated in coin. 

It is a sorry confession to make, but it is nevertheless 
the truth, that, if we compare our American universities, 
in point of literary or scientific productiveness, with those 
of the Old "World, they will appear lamentably deficient. 
Let me add, however, that this deficiency arises not from 
any want of proper aims in our scholars, but simply from 
the circumstance that our people do not sufficiently ap- 
preciate the value of the higher forms of literary and 
scientific work to bear the burden which the production 
necessary entails. Scholars must live, as well as other 
men, and in a style which is in harmony with their sur- 
roundings and cultivated tastes, and their best efforts can 
not be devoted to the extension of knowledge unless they 
are relieved from anxiety in regard to their daily bread. 



REFORM REQUIRED. 51 

In our colleges the professors are paid for teaching 
and for teaching only, while in a foreign university the 
teaching is wholly secondary, and the professor is ex- 
pected to announce in his lectures the results of his own 
study, and not the thoughts of other men. Until the 
whole status of the professors in our chief universities 
can be changed, very little original thought or investiga- 
tion can be expected, and these institutions can not be- 
come what they should be, the soul of the higher life of 
the nation. 

It is in your power, however, to bring about this 
change, but the reform can be effected in only one way. 
You must give to your universities the means of sup- 
porting fully and generously those men of genius who 
have shown themselves capable of extending the boun- 
daries of human knowledge, and demand of them, only, 
that they devote their lives to study and research, and let 
me assure you that no money can be spent which will 
yield a larger or more valuable return. 

If you do not look beyond your material interests, the 
higher life of the nation, which you will thus serve to 
cherish and foster, will guard your honor and protect 
your home ; and, on the other hand, what can you expect 
in a nation whose highest ideal is the dollar or what 
the dollar will buy, but venality, corruption, and ultimate 
ruin? 



52 TIIE NOBILITY OF KNOWLEDGE. 

But, rising at once to the noblest considerations, and 
regarding only the welfare of your country and the edu- 
cation of your race, what higher service can you render 
than by sustaining and cherishing the grandest thought, 
the purest .ideals, and the loftiest aspirations which 
humanity has reached, and making your universities the 
altars where the holy fire shall be kept ever burning 
bright and warm % 

Do you think me an enthusiast ? Look back through 
history, and see for yourselves what has made the nations 
great and glorious. Why is it that, after twenty cen- 
turies, the memory of ancient Greece is still enshrined 
among the most cherished traditions of our race? Is it 
not because Homer sang, Phidias wrought, and Plato, 
Aristotle, Demosthenes, Thucydides, with a host of 
others, thought and wrote \ Or, if for you the military 
exploits of that classic age have the greater charm, do 
not forget that, were it not for Grecian literature, Ther- 
mopylae, Marathon, and Salamis would have been long 
since forgotten, and that the bravery, self-devotion, and 
patriotism which these names embalm were the direct 
fruits of that higher life which those great thinkers illus- 
trated and sustained. 

And, coming down to modern times, what are the 
shrines in our mother country which we chiefly vener- 
ate, and to which the transatlantic pilgrim oftenest di- 



GALYANTS EXPERIMENTS. 53 

rects his steps? Is it lier battlefields, her castles and 
baronial halls, or sneh spots as Stratford-on-Avon, Ab- 
botsford, and Rydal Mount? Why, then, will we not 
learn the lesson which history so plainly teaches, and 
strive for those achievements in knowledge and mental 
culture which will be remembered with gratitude when 
all local distinctions and political differences shall have 
passed away and been forgotten ? 

While I was considering the line of discourse which 
I should follow on this occasion, an incident occurred 
suggesting an historical parallel, which will illustrate, 
better than any reflections of mine, the truth I would 
enforce. The ship Faraday arrived on our coast after 
laying over the bed of the Atlantic another of those elec- 
tric nerves through which pulsate the thoughts of two 
continents, and as I read the description of that noble 
ship, fitted out with all the appliances which modern 
science had created to insure the successful accomplish- 
ment of the enterprise, I remembered that not a century 
had elapsed since the first obscure phenomena were ob- 
served, whose conscientious study, pursued with the un- 
selfish spirit of the scientific investigator, had led to these 
momentous results, and my imagination carried me back 
to an autumn day of the year 1786, in the old city of 
Bologna, in Italy, and I seemed to assist at the memo- 
rable experiment which has associated the name of Aloy- 



54 THE NOBILITY OF KNOWLEDGE. 

sius Galvani with, that mode of electrical energy which 
flashes through the wire cords that now unite the four 
quarters of the globe. 

Galvani is Professor of Anatomy in the University 
of Bologna, and there is hanging from the iron balcony 
of his house a small animal preparation, which is not an 
unfamiliar sight in Southern Europe, where it is regard- 
ed as a delicacy of the table. It is the hind-legs of a 
frog, from which the skin had been removed, and the 
great nerve of the back exposed. Six years before, his 
attention had been called to the fact that the muscles of 
the frog were convulsed by the indirect action of an elec- 
trical machine, under conditions which he had found 
very difficult to interpret. He had connected the phe- 
nomenon with a theory of his own : that electricity — that 
is, common friction electricity, the only mode of electri- 
cal action then known — was the medium of all nervous 
action; and this had led him into a protracted investi- 
gation of the subject, during which he had varied the 
original experiment in a thousand ways, and he had now 
suspended the frog's legs to the iron balcony, in order to 
discover if atmospheric electricity would have any effect 
on the muscles of the animal. 

Galvani has spent a long day in fruitless watching, 
when, while holding in his hand a brass wire, connected 
with the muscles of the frog, he rubs the end, apparently 



GALVANI'S EXPERIMENTS. 55 

listlessly, against the iron railing, when, lo! the frog's 
legs are convulsed. 

The patient waiting had been rewarded, for this ob- 
servation was the beginning of a line of discovery which 
was ere long to revolutionize the world. But Galvani 
was not destined to follow far the new path he had thus 
opened. The remarkable fact observed was this: The 
convulsions of the frog's legs could be produced without 
the intervention of electricity, or, at least, of the one 
kind of electricity then known, and Galvani soon found 
out that the only condition necessary to produce the re- 
sult was, that the nerve of the frog should be connected 
with the muscle of the leg by some good electrical con- 
ductor. 

But, although Galvani followed up this observation 
with the greatest zeal, and showed remarkable sagac- 
ity throughout his whole investigation, yet he was too 
strongly wedded to his own theory to interpret correctly 
the facts he observed. He supposed, to the end of his 
life, that the whole effect was caused by animal electric- 
ity flowing through the conductor from the nerve to the 
muscle, and his experiments were chiefly interesting to 
himself and to his contemporaries from the light they 
were supposed to throw on the mysterious principle of 
life. We now know that animal electricity played only 
a small part in the phenomena he observed, and that the 



56 THE NOBILITY OF KNOWLEDGE. 

chief effects were due to a cause of which he was wholly 
ignorant. 

Galvani published his observations in 1791, in a 
monograph entitled " The Action of Electricity in Mus- 
cular Motion." This publication excited the most 
marked attention, and, within a year, all Europe was ex- 
perimenting on frogs' legs. The phenomena were every- 
where reproduced, but Galvani' s explanation of the phe- 
nomena was by no means so universally accepted. His 
theory was controverted in many quarters, and by no one 
more successfully than by Alexander Yolta, Professor of 
Physics in the neighboring University of Pavia. 

Yolta, while admitting, with Galvani, that the muscu- 
lar contractions were caused by electricity, explained the 
origin of the electricity in a wholly different way. Ac- 
cording to Yolta, the electricity originated not in the 
animal, but in the contact of the dissimilar metals or 
other materials used in the experiment. This difference 
of opinion led to one of the most remarkable controver- 
sies in the history of science, and for six years, until his 
death in 1798, Galvani was occupied in defending his 
theory of animal electricity against the assaults of his dis- 
tinguished countryman. 

This discussion created the liveliest interest through- 
out Europe. Every scholar of science took sides with 
one or the other of these eminent Italian philosophers, 



GALVANI AND YOLTA. 57 

and the scientific world became divided into the school 
of Galvani and the school of Yolta. Yet, so far at least 
as the fundamental experiment was concerned, both were 
wrong. The electricity came neither from the body of 
the frog nor from the contact of dissimilar kinds of mat- 
ter, but was the result of chemical action, which both 
had equally overlooked. 

But, nevertheless, the controversy led to the most 
important results: for Yolta, while endeavoring to sus- 
tain his false theory by experimental proofs, was led to 
the discovery of the Yoltaic pile, or, as we now call 
it, the Yoltaic battery, an instrument whose influence 
on civilization can be compared only with the printing- 
press and the steam-engine. Yet, although the whole 
action of the battery was in direct contradiction to his 
pet theory, still, to the last, Yolta persistently defended 
the erroneous doctrine he had espoused in his contro- 
versy with Galvani thirty years before, and he died in 
1827, without realizing how great a boon he had been 
instrumental in conferring on mankind ; so true it is that 
Providence works out his bright designs even through 
the blindness and mistakes of man. 

But there is another lesson to be learned from this 
history, which can not be too often rehearsed in this self- 
sufficient age, which boasts so proudly of its practical 
wisdom. There were, doubtless, many practical men in 



58 THE NOBILITY OF KNOWLEDGE. 

that city of Bologna to smile at their sage professor, who 
had spent ten long years in studying, to little apparent 
purpose, the twitchings of frogs' hind-legs, and there 
was many a jest among the courtiers of Europe at the 
expense of the learned philosophers who "wasted" so 
much time in discussing the cause of such trivial phe- 
nomena. But how is it now ? 

Less than a century has passed since Galvani's death, 
and in a small hut on the shores of Yalentia Bay may 
be seen one of the most skillful of a new class of prac- 
tical men, representing a profession which owes its ori- 
gin to Gal van i and Yolta. The electrician is watching 
a spot of light on the scale of an instrument which is 
called a galvanometer. Since the fathers fell asleep, the 
field of knowledge which they first entered has spread 
out wider and wider before the untiring explorers who 
have succeeded them. Oersted and Seebeck, Arago and 
Ampere, Faraday and our own Henry, have made won- 
derful discoveries in that field ; and other great men, 
like Steinheil, Wheatstone, Morse, and Thomson, have 
invented ingenious instruments and appliances, by which 
these discoveries might be made to yield great practical 
results. 

The spot of light, which the electrician is watching, 
is reflected from one of the latest of these inventions, the 
reflecting galvanometer of Thomson. He and his assist- 



GREAT RESULTS. 59 

ants had been watching by turns the same spot for several 
days, since the Great Eastern had steamed from the bay, 
paying out a cable of insulated wire. These electricians 
had no anxiety as to the result, for daily signals had been 
exchanged between the ship and the shore, as hundreds 
after hundreds of miles of this electrical conductor had 
been laid on the bed of the broad ocean. The coast of 
Newfoundland had already been reached, and they were 
only waiting for the landing of the cable at the now far- 
distant end. 

At length the light quivers, and the spot begins to 
move. It answers to concerted signals. And soon the 
operator spells out the joyful message. The ocean has 
been spanned with an electric nerve, and the New World 
responds to the greetings of the Old. 

Here is something practical, which all can appreciate, 

and all are ready to honor. We honor the courage which 

conceived, the skill which executed, and, above all, the 

success which crowned the undertaking. But do we not 

forget that professor of Bologna, with his frogs' legs, 

who sowed the seed from which all this has sprung ? He 

labored without hope of temporal reward, stimulated by 

the pure love of truth, and the grain which he planted 

has brought forth this abundant harvest. Do we not 

forget, also, that succession of equally noble men, Yolta, 

and Oersted, and Faraday, with many other not less de- 
5 



60 THE NOBILITY OF KNOWLEDGE. 

voted investigators of electrical science, without whose 
unselfish labors the great result never could have been 
achieved j Such men, of course, need no recognition at 
our hands, and I ask the question not for their sakes, but 
for ours. The intellectual elevation of the lives they led 
was their all-sufficient reward. 

It is, however, of the utmost importance for us, citi- 
zens of a country with almost unlimited resources, that we 
should recognize what are the real springs of true na- 
tional greatness and enduring influence. In this age of 
material interests, the hand is too ready to say to the 
head, " I have no need of thee " ; and, amid the ephem- 
eral applause which follows the realization of some tri- 
umph over matter, we are apt to be deceived, and not 
observe whence the power came. "We associate the great 
invention with some man of affairs man who overcame 
the last material obstacle, and who, although worthy of 
all praise, probably added very little to the total wealth 
of knowledge of which the invention was an immediate 
consequence ; and, not seeing the antecedents, we are apt 
to underrate the part which the student or scientific in- 
vestigator may have contributed to the result. 

It is idle, for example, to speak of the electric tele- 
graph as invented by any single man. It was a growth 
of time, and many of the men who contributed to win 
this great victory of mind over space " builded far better 



KNOWLEDGE AND INVENTION. 61 

than they knew." As I view the subject, that invention 
is as much a gift of Providence as if the details had been 
supernaturally revealed. But, whatever may be our 
speculative views, it is of the utmost importance to the 
welfare of our community that we should realize the fact 
that purely theoretical scientific study, pursued for truth's 
sake, is the essential prerequisite for such inventions. 
Knowledge is the condition of invention. The old Latin 
word invenio signifies to meet with, as well as to find, 
and these great gifts of God are met with along the 
pathway of civilization ; but the throng of the world 
passes them unnoticed, for only those can recognize the 
treasure whose minds have been stored with the knowl- 
edge which the scholar has discovered and made known. 

If, then, as no one will deny, science and scholarship 
are the powers by which improvements in the useful arts 
are made, I might appeal to your self-interest to support 
and cherish them. But I should despise myself for 
appealing to such a motive, and you for requiring it. 
The supreme importance of science and scholarship to a 
nation does not depend in the least on the circumstance 
that important practical results may follow. When, as 
in the case of Galvani's frogs, they come in the order of 
Providence, let us thank God for them as a gift which 
we had no right either to expect or demand. Science, if 
studied successfully, must be studied for the pure love of 



02 THE NOBILITY OF KNOWLEDGE. 

truth ; and, if we serve her solely for mercenary ends, 
her truths, the only gold she offers, will turn to dross in 
our hands, and we shall degrade ourselves in proportion 
as we dishonor her. 

Galvani, and Yolta, and Oersted, who discovered the 
truths of which the electric telegraph is a simple appli- 
cation, sure to be made as soon as the time was ripe, 
are not the less to be honored because they died before 
the fullness of that time had come. "We honor them 
for the truths they discovered, and the lustre of their 
consecrated lives could be neither enhanced nor im- 
paired by subsequent events ; and it is because I am 
persuaded that such lives are the salt of the world, the 
saviours of society, that I would lead you to cherish and 
sustain them ; and, that I may enforce this conclusion, 
allow me to ask your attention to another historical in- 
cident, which presents a striking parallelism to the last. 

I must take you back to a period which we, of a 
nation born but yesterday, regard as distant, but which 
was one of the most noted epochs of modern history — 
the age of Luther and the Reformation. I must ask you 
to accompany me to the small town of Allenstein, near 
Frauenberg, in Eastern Prussia, where, on May 23, 1543, 
there lay dying one of the great benefactors of mankind. 

This man, old at seventy years, " bent and furrowed 
with labor, but in whose eye the fire of genius was still 



STORY OF COPERNICUS. 63 

glowing," was then known as one of the most learned 
men of his time. Doctor of medicine as well as of the- 
ology, Canon of Frauenberg, Honorary Professor of Bo- 
logna and Kome, while devoting his leisure to study, he 
had passed a life of active benevolence in administering 
to the bodily as well as the spiritual wants of the ignorant 
people among whom his lot had been cast. He was also 
a great mechanical genius, and, by various labor-saving 
machines, of his own invention, he had contributed 
greatly to the welfare of the surrounding country. 

But the superstitious peasants, although they had hith- 
erto reverenced the great man as their best friend and 
benefactor, had been recently incited by his enemies and 
rivals in the church to curse him as a heretic and a wizard. 
A few days back he had been the unwilling witness of one 
of those out-of-door spectacles, so common at that time, 
in which his scientific opinions had been travestied, his 
charities ridiculed, and his devoted life made the object 
of slander and reproach. This ingratitude of his flock had 
broken his heart, and he could not recover from the blow. 

The occasion of this outburst of fanaticism was the 
approaching publication of a work in which he had dared 
to question the received opinions of theologians and 
schoolmen, in regard to cosmogony. He had, forsooth, 
denied that the visible firmament was a solid azure- 
colored shell, to which the sun and planets were fastened, 



64 TIIE NOBILITY OF KNOWLEDGE. 

and through whose opened doors the rain descended. He 
had proved that the sun was the center of the system, 
around which the earth and planets revolved, and, with 
his clear scientific vision, he had been able to gain 
glimpses, at least, of the grand conceptions of modern 
astronomy: For this man was Nicolas Copernicus, and 
the expected book was his great work — "De Orbium 
Ccelestium Eevolutionibus " — destined to form the broad 
basis of astronomical science. 

The work was printing at Nuremberg, and the last 
proofs had been returned; but reports had come that 
a similar outburst of fanaticism was raging at that place, 
that a mob had burned the manuscript on the public 
square, and had threatened to break the press should the 
printing proceed. But, thanks to God! the old man 
was not to die before the hour of triumph came. "While 
still conscious, a horse, covered with foam, gallops to the 
door of his humble dwelling, and an armed messenger 
enters the chamber, who, breathless with haste, places 
in the hands of the dying man a volume still wet from 
the press. He has only strength to return a smile of 
recognition, and murmur the last words : 

" Nunc dimittis servum taum, Domine." 

Grand close of a noble life ! The seed has been sown — 
what could we desire more ? 



DISCOVERY OF NEPTUNE. 65 

Again the centuries roll on — not one, but three — 
while the seed grows to a great tree, which overshadows 
the nations. Great minds have never been wanting to 
cherish and prune it, like Tycho Brahe and Kepler, Gali- 
leo and Newton, Laplace and Lagrange ; and although at 
times some, while lingering in the deep shade of the foli- 
age, may have lost sight of the summit, the noble tree 
has ever pointed upward to direct aspiration and encour- 
age hope. 

On the evening of the 24th of September, 1846, in 
the Observatory of Berlin, a trained astronomical ob- 
server was carefully measuring the position of a faint 
star in the constellation Capricorn. Only the day before, 
he had received from Le Verrier a letter announcing the 
result of that remarkable investigation which has made 
the name of this distinguished French astronomer so 
justly celebrated. By the studies of the great men who 
succeeded Copernicus, his system had become so perfected 
as to enable the astronomer to predict, with unerring cer- 
tainty, the paths of the planets through the heavens. 
But there was one failing case. The planet Uranus, then 
supposed to be the outer planet of the solar system, 
wandered from the path which theory assigned to it; 
and although the deviations were but small, yet any dis- 
crepancy between theory and observation in so accurate 
a science as astronomy could not be overlooked. 



G6 THE NOBILITY OF KNOWLEDGE. 

Long before this, the hypothesis had been advanced 
that the deviations were caused by the attractive force 
of an unseen and still more distant planet; but, as no 
such planet had been discovered, the hypothesis had re- 
mained until now wholly barren. The hypothesis, how- 
ever, was reasonable, and furnished the only conceiv- 
able explanation of the facts; and, moreover, if true, 
the received system of astronomy ought to be able to as- 
sign the position and magnitude of the disturbing body, 
the magnitude and direction of the displacements being 
given. 

This possibility was generally appreciated by astrono- 
mers, and the very great length and difficulty of the 
mathematical calculation which the investigation in- 
volved was probably the reason that no one had hitherto 
undertaken it. Le Verrier, however, had both the cour- 
age and the youthful strength required for the work. 
And now the great work had been done; and, on the 
18th of September, Le Yerrier had sent to the Observ- 
atory of Berlin his communication announcing the final 
result, namely, that the planet would be found about 5° 
to the east of the star Delta of Capricorn. 

The letter containing this announcement was received 
by Galle, at Berlin, on the 23d, and it was Galle whom 
we left measuring the position of that faint star on the 
evening of the 24th. It so happened that a chart of that 



VALUE OF TEE DISCOVERY. 67 

portion of the heavens had recently been prepared by 
the Berlin Observatory, and was on the eve of publica- 
tion ; and, on the very evening he received the letter, 
Galle had f onnd, near the position assigned by Le Ter- 
rier, a faint star, which was not marked on this chart. 
The object differed in appearance from the surrounding 
stars, but still it was perfectly possible that it might be 
a fixed star which had escaped previous observation. 

But, if a fixed star, its position in the constellation 
would not vary, while, if a planet, a single night would 
show a perceptible change of place. Hence, you may 
conceive of the interest with which Galle was measuring 
anew its position on the evening of the 24th. 

The star had moved, and in the direction which the- 
ory indicated; and for once, at least, the world rang 
with applause at a brilliant scientific conquest from which 
there was not one cent of money to be made. Yet, was 
that conquest any less important to the world ? What 
had it secured 1 It had confirmed the theory of astron- 
omy which Copernicus and his successors had built up, 
and it had clinched the last nail in the proof that those 
grand conceptions of modern astronomy, now household 
thoughts, are realities, and not dreams. Certainly no 
military conquest can compare with this. 

Do not smile at the enthusiasm which rates so high 
a purely intellectual achievement? Go out with me 



68 THE NOBILITY OF KNOWLEDGE. 

under the heavens, in some starlight night, and, looking 
up into the depths of space, recall the truths you have 
learned in regard to that immensity, and allow the imag- 
ination free scope as it stretches out into the infinitudes 
of time, space, and power, carrying the mind on, bound 
by bound, through the limitless expanse, until even the 
imagination refuses to follow, and fairly quails before 
the mighty form of the Infinite, which rises to confront 
it ! Remember now that your forefathers, of only a few 
centuries back, saw there nothing but a solid dome hem- 
ming in the earth and skies, and that you are able to 
look upon this grand spectacle only because great minds 
have lived who have opened your intellectual eyes ; and 
then answer me, is not this result worth all the labor, all 
the sacrifice, all the treasure it has .cost ? 

Every educated man, who has not sold his birthright 
for a mess of pottage, lives a grander and nobler life, 
because the great astronomers have thought and taught, 
and this elevation of human life is the greatest achieve- 
ment of which man can boast. Before it all material 
conquests appear of little worth, and the lustre of all 
military or civil glory grows dim. Cherish this intel- 
lectual life; foster it; sustain it; do what you can by 
your own spirit and influence, and, if you are blessed 
with riches, give of your abundance to support and en- 
courage those who, by genius, talent, and devotion, will 



INTELLECTUAL LIFE. 69 

widen the intellectual kingdom. Be assured yon will 
thus help to confer an inestimable boon on your race and 
on your country ; and the influence for good will not be 
felt by the intellectual life of the nation only. That cor- 
ruption which is now festering at the heart of our body 
politic, and threatening its destruction, can in no way be 
fought and conquered so effectually as by keeping con- 
stantly before the nation noble and high ideals; for, 
where the higher life is cherished and honored, the mer- 
cenary and sensual motives of action, which both invite 
and shield corruption, lose much of their force and 
power. 

But you may tell me that there is a life higher than 
the intellectual life, and that I have ascribed to science 
and scholarship influences which come only from a source 
which I have forgotten, or left out of view. My friends, 
all truth is one and inseparable, and I have therefore 
made no distinction in this address between the truths 
of science and truths of religion. The grand old word 
knowledge, as I have used it, includes both, and, in just 
the proportion that you reverence religion, you must rev- 
erence also true science. All truth is God's truth, and, 
in praying for the coming of his kingdom, you certainly 
do not expect that Nature will be divorced from Grace. 
If the truths of religion required a special revelation, it 
must be expected that they would transcend human in- 



70 THE NOBILITY OF KNOWLEDGE. 

telligence. These very conditions imply conflict, but the 
conflict comes not from the knowledge, but from the 
ignorance and conceit of men ; and the only proper atti- 
tude for the devout scholar is "to labor and to wait." 
And what more wonderful confirmation could we have 
of the essential unity of the two phases of truth than is 
to be found in the fact that the characteristic of science, 
which I have been endeavoring to illustrate in this ad- 
dress, is the great prominent feature of Christianity? 
Christianity was revealed in a life, and ever abides a life 
in the soul of man, to purify, ennoble, and redeem hu- 
manity. 

"And so the Word had breath, and wrought, 

With human hands, the creed of creeds, 

In loveliness of perfect deeds, 
More strong than all poetic thought — 

* Which he may read that binds the sheaf, 
Or builds the house, or digs the grave, 
And those wild eyes that watch the wave, 
In roarings round the coral reef. 1 ' 



in. 

THE ELEMENTARY TEACHING OF 
PHYSICAL SCIENCE. 

An Address to the Schoolmasters of Boston^ delivered 
February 4, 1878. 

I felt a great reluctance at accepting the invitation 
of your excellent superintendent to address you on this 
occasion ; for, although I could claim an unusually long 
experience in presenting the elements of physical science 
to college students, I was fully conscious that I knew 
little of the conditions under which such subjects must 
be studied, if at all, in the elementary schools, and was 
therefore in danger of appearing in a capacity which I 
should most sedulously shun, that of a babbler about 
impracticable theories of education. It is very easy to 
criticize another man's labor, and such criticisms, how- 
ever plausible, do the grossest injustice when, as is often 
the case, they leave out of view the necessary conditions 



72 THE ELEMENTARY TEACHING OF PHYSICAL SCIENCE. 

and limitations under which the work must be done. 
While, however, I felt most keenly my incapacity to deal 
with many of the practical problems which you have to 
solve, yet, on consideration, I concluded that it was my 
duty under the circumstances to state as clearly and 
forcibly as I could the very definite opinions which I 
had formed on the subject you are discussing, knowing 
that you will only give such weight to these opinions as 
your mature judgment can allow. In stating the results 
of my experience, I can not avoid a certain personal ele- 
ment, which would be wholly inexcusable were it not 
that the facts, as I think you will admit, form the basis 
of my argument. 

I am a Boston boy, born in this immediate neighbor- 
hood, and fitted for college at the " Latin School." It so 
happened that, while I was very unsuccessfully endeavor- 
ing to commit to memory, in the old school-house on 
School Street, Andrews and Stoddard's Latin grammar, 
not one word of which I could understand, the " Lowell 
Institute " lectures were opened at the " Odeon" on Con- 
gress Street. At those lectures I got my first taste of 
real knowledge, and that taste awakened an appetite 
which has never yet been satisfied. As a boy, I eagerly 
sought the small amount of popular science which the 
English literature of that day afforded ; and I can now 
distinctly recall almost every page of Mrs. Marcet's " Con- 



EARLY EXPERIENCE. 73 

versations on Chemistry," which was the first book on 
my science that I ever read. More to the point than 
this, a boy's pertinacity, favored by a kind father's indul- 
gence, found the means of repeating, in a small way, 
most of the experiments first seen at the Lowell Institute 
lecture ; and thus it came to pass that, before I entered 
college, I had acquired a real, available knowledge of the 
facts of chemistry; although, with much labor and in- 
tense weariness, I had gained only a formal knowledge of 
those subjects which were then regarded as the only 
essential preparation for the college course. In college, 
my attention was almost exclusively devoted to other 
studies — for, in my day at Cambridge, chemistry was one 
of the lost arts. But when, the year after I graduated, I 
was most unexpectedly called upon to give my first 
course of lectures, the only laboratory in which I had 
worked was the shed of my father's house on Winthrop 
Place, and the only apparatus at my command was what 
this boy's laboratory contained. With these simple tools, 
or, as I should rather say, because they were so simple, I 
gained that measure of success which determined my 
subsequent career. 

I feel that I owe you a constant apology for these 
personal details, and I should not be guilty of them did I 
not believe that they establish two points more conclu- 
sively than I could prove them in any other way. First, 



^4 THE ELEMENTARY TEACHING OF PHYSICAL SCIENCE. 

that it is perfectly possible for a child before fifteen years 
of age to acquire a real and living knowledge of the 
fundamental facts of nature on which physical science is 
based. Secondly, that this knowledge can be effectually 
gained by the use of the simplest tools. Let me add 
that this is not a question of natural endowments or spe- 
cial aptitudes, for every one who has studied from the 
love of knowledge has had the same experience ; and I 
do not believe that, if my first taste of real knowledge 
had been of history, nay, I will even say, of philology, 
instead of chemistry, the circumstance would have mate- 
rially influenced my success in life, however different the 
direction into which it might have turned my study. My 
early tastes were utterly at variance with all my sur- 
roundings and all my inheritances, and were simply 
determined by the accident which first satisfied that natu- 
ral thirst for knowledge which every child experiences to 
a greater or less degree — a desire most rudely repressed 
in our usual methods of teaching. 

My bitter experience as a pupil in the Boston Latin 
School and my subsequent more fortunate experience of 
thirty years as a teacher in Harvard College have im- 
pressed me most profoundly with the conviction that the 
only way to arouse and sustain a love for knowledge in 
children is to cultivate their perceptive faculties. To 
present the rudiments of knowledge to immature minds 



OBJECT TEACHING. 75 

in an abstract form, whether the subject be grammar or 
physical science, is, in my judgment, not only culpable 
folly, but also downright wrong. And, if, to those who 
have been accustomed to the long established routine of 
our public school, my opinions may appear revolutionary 
and extreme, I am, nevertheless, sure that they would 
receive the universal assent of the men whom all would 
recognize as the foremost scientific teachers of the world. 
I can well remember that when, many years ago, the late 
Professor Agassiz declared in my hearing that he would 
have no text-books used in his museum, I thought his 
plan of pure object-teaching chimerical in the extreme, 
and yet experience has not only convinced me of the wis- 
dom of his judgment in regard to the teaching of natural 
history, but brought me to a similar conclusion in regard 
to the elementary teaching both of natural philosophy 
and of chemistry. 

Allow me then to express my firm persuasion that 
it is not only useless but injurious to the education of 
young minds to present to them at the outset any de- 
partment of physical science as a body of definitions, 
principles, laws, or theories; and that in elementary 
schools only such facts should be taught as can be veri- 
fied by the experience of the pupil, or by such simple 
experiments as the pupils can try for themselves. The 

usual method of committing by heart the words of a 
6 



76 THE ELEMENTARY TEACHING OF PHYSICAL SCIENCE. 

school-book, and repeating them at the dictation of a 
teacher, may afford a good exercise for the memory, but 
it is absurd to regard such a task as a lesson in physical 
science, and this kind of study can be spent with vastly 
greater profit on the spelling-book. 

There is one department of physical science which 
has been taught in this absurd way in our schools from 
time immemorial. I refer, of course, to the study of geog- 
raphy, and I leave for you to judge whether the result 
is worth the one hundredth part of the toil and drudgery 
spent in obtaining it. Let us suppose that your child 
is able to give you the names of all the rivers, bays, and 
capes from Greenland to Patagonia, how much more 
does that child know of the structure and social relations 
of this globe on which its lot has been cast than it did 
before this senseless feat was attempted, a feat, more- 
over, to which only a child's memory would be equal ? 
And, when you turn to your own experience, what is the 
outcome of all the time and labor spent on geography ? 
Is it not solely just that portion of your knowledge 
which, in spite of the system, was direct object-teaching — 
the images you insensibly acquired from the maps and 
pictures in the school-books ? 

But there is a very different way of teaching geog- 
raphy, by which the study may be made a pleasure, not 
a task. The teacher does not begin with abstract defini- 



TEACHING OF GEOGRAPHY. 77 

tions of rivers, and bays, and oceans, which convey no 
definite meaning to a child, but with Charles River, Bos- 
ton Harbor, and the Atlantic Ocean, which are to him 
real things, however imperfect his conceptions of their 
extent. The child is first shown, not a map of the globe, 
which he can not by any possibility understand, but a 
map of a very limited region around his own home. He 
is taught how to find the north and south, the east and 
west directions. He is encouraged to make excursions 
to verify the map, or to add to its details, and such ex- 
cursions may be made to have for him all the zest of 
voyages of discovery ; and when thus the rudiments of 
geographical science have been mastered, not in technical 
terms, but in substance,.. then the teacher may begin to 
expand the horizon of the pupil's knowledge, judiciously 
omitting details in proportion as distance increases, until 
at length the general survey embraces the globe. Of 
course, such teaching as this can only be given orally 
with the help of proper apparatus, such as wall maps, 
and globes, and photographs. It must take the inter- 
rogative form, and the questions should be directed to 
bring out the child's already acquired knowledge, and to 
lead him to observe facts which had hitherto escaped his 
notice. "What a child reads in a book, or even what you 
tell him, is never one half learnt, unless his interest is 
aroused. But what a child observes for himself he never 



78 THE ELEMENTARY TEACHING OF PHYSICAL SCIENCE. 

forgets, and when you have thus aroused his interest you 
can associate a large number of facts with one observa- 
tion, and these all crystallize in his memory around this 
nucleus. 

This is no mere theorv, no untried method which I 
am advocating. So far from it, I am describing the 
precise method which has been used for many years in 
Germany, where the science of education is far better 
understood than with us, and where economy both of 
time and labor in teaching is most carefully studied. If 
our school committees could attend and understand a 
single exercise in geography, such as are daily given in 
the elementary schools of Prussia, I am sure that at least 
one form of child torture would soon disappear from the 
primary schools of this country. Indeed, I already see 
evidence of a growing public opinion on this subject, an 
effect which I trace in no small measure to the influence 
of the Department of Education of the Exhibition at 
Philadelphia in 1876. 

That which is true of geography applies with still 
greater force to such subjects as physics and chemistry, 
since the abstract conceptions which these sciences in- 
volve are more abstruse, and the language by which the 
conceptions are expressed or defined far less plain than 
is the case with the older and more descriptive branch 
of knowledge. Hence, as sciences, properly so called, 



TEACHING OF MECHANICS. 79 

that is, as philosophical systems, they have no place what- 
ever in elementary education. But, underlying these 
systems, there is a great multitude of phenomena which 
a child can be led to observe and apprehend as readily as 
the facts of geography. Take that subject — mechanics — 
which our ordinary school-books very philosophically but 
most unpractically place at the beginning of what they 
call "Natural" Philosophy. How many of the funda- 
mental facts of this difficult subject can be made familiar 
to a child ? Select, as an example, Newton's " First Law 
of Motion." Suppose you make a boy memorize the 
ordinary rule, " Every body continues in a state of rest 
or of uniform motion -in a straight line until acted upon 
by some external force," how much will he know about 
it ? Suppose you make him do a lot of problems involv- 
ing distances, velocities, and times, will he know any 
more about it ? But ask him, " Can you pitch a ball as 
well as your playmate % " and he answers at once, " No ; 
John is stronger than I am." And then, if again you 
ask, " Can you catch John's ball ? " he will probably re- 
ply, " Of course, not ! It requires a boy as strong as 
John to catch his balls." And thus, by a few well-direct- 
ed questions, you would bring that boy to learn a lesson 
which he would never forget, and which he would recall 
every time he played base-ball ; namely, that John's swift 
balls could not be set in motion without an expenditure 



80 THE ELEMENTARY TEACHING OF PHYSICAL SCIENCE. 

of a definite amount of muscular effort, and could not be 
stopped without the exertion of an equal amount of 
what, after a while, you could get him to call force. 
From the ball you would naturally pass to the railroad 
train or the steamboat, and I should not wonder if, with 
a little patience, you could bring even a boy to under- 
stand that motion can not be maintained against a resist- 
ance, in other words, that work can not be done with- 
out a constant expenditure of muscular effort, or of some 
other source of power ; and it is a fond hope of mine 
that by the time these boys grow into men our intelli- 
gent ISTew England community might become so far 
educated in the elementary principles of mechanics that 
no self-sustained motors, nor other mechanical nostrums 
which claim to have superseded the primeval curse — if 
that law was a curse, which compels man to earn his 
bread with the sweat of his brow — will receive the sanc- 
tion of our respectable journals ; and then — if they have 
not previously learned the lesson by dire experience — we 
may hope to persuade our people of the parallel and 
equally elementary principle of political economy, that 
value can not be legislated into rags. 

But, my friends, our subject gives no occasion for 
banter, and presents aspects too serious to be treated 
lightly or in jests. As inhabitants of a not over-fruit- 
ful land, and, therefore, members of a community which 



"ICH DIEN." 81 

must excel, if at all, solely by its enterprise and intelli- 
gence, we have a duty to our children which we can not 
avoid, if we would, and for which we shall be held re- 
sponsible by our posterity. These children are entering 
life surrounded not only by all the wonders and glories 
of nature, but, also, by giant conditions, which, whether 
stationed on their path as a blessing or a curse, will in- 
evitably strike if their behests are not obeyed. So far as 
science has been able to define these giant forms, it is our 
duty, as it is our privilege, to point them out to those we 
are bound to protect and guide ; and in many cases it is 
in our power to change the curse into a blessing, and to 
transform the destructive demon into a guardian angel. 
After that command of language which the necessities 
of civilized life imperatively require, there is no acquisi- 
tion which we can give our children that will exert so 
important an influence on their material welfare as a 
knowledge of the laws of nature, under which they must 
live and to which they must conform; and throughout 
whose universal dominion the only question is whether 
men shall grovel as ignorant slaves or shall rule as intel- 
ligent servants. Yes ; rule by obeying. " Ich Dien " ; 
for only under that motto, which, five hundred years ago, 
the great Black Prince bore so victoriously through the 
fields of Cressy and Poitiers, can man ever rule in Nat- 
ure's kingdom. 



82 THE ELEMENTARY TEACHING OF PHYSICAL SCIENCE. 

I regard it, therefore, as the highest duty and the 
most enlightened self-interest of a community like this 
to provide the best means for the instruction of its chil- 
dren in the elements of physical science ; and I was, there- 
fore, most anxious to do all in my power to second the 
enlightened efforts of your eminent Superintendent in 
this direction. You must remember, however, that the 
best tools are worthless in themselves, and can secure no 
valuable results unless judiciously used. Indeed, there is 
danger in too many tools, and I have a great horror of 
that array of brass-work which is usually miscalled " phil- 
osophical " apparatus. The greater part of this is, in my 
opinion, a mere hindrance to the teacher, because it at 
once erects a barrier between the scholar and the simple 
facts of nature, and the child inevitably associates with 
the phenomenon illustrated some legerdemain, and looks 
on your experiments very much as he would on the exhi- 
bition of a Houdin or a Signor Blitz. The secret of suc- 
cess in teaching physical science is to use the simplest 
and most familiar means to illustrate your point. 

When a very young man I was favored with an in- 
troduction to Michael Faraday, and had the privilege of 
attending a portion of a course of lectures which this 
noble man was then in the habit of giving every Christ- 
mas season to a juvenile auditory at the Royal Institution 
of London. As a boy, I had become familiar with lee- 



FARADAY'S EXAMPLE. 83 

tures on chemistry at the Lowell Institute, where they 
did not lack the pomp of circumstance or the display of 
apparatus, and I had come to associate these elements 
with the conditions of success in lectures of this kind. 
What, then, was my surprise to find Faraday, the ac- 
knowledged leader of the world in his science, and who 
had every means of illustration at his command, using 
the plainest language and the simplest tools. When, in 
my youthful admiration at the result, I expressed, after 
one of the lectures, my surprise at the simplicity of the 
means employed, the great master replied : " That is the 
whole secret of interesting these young people. I always 
use the simplest means, but I never leave a point not il- 
lustrated. If I mention the force of gravitation I take 
up a stone and let it drop." At this distance of time, I 
can not be sure that I quote his exact language, but the 
lesson and the illustration I could not forget ; and to this 
lesson, more than to any other one thing, I owe whatever 
success I have had as a teacher of physical science. 

I repeat, therefore, it is not only useless but in- 
jurious in the education of young minds to present 
any department of physical science as a body of defi- 
nitions, principles, laws, or theories ; and that in ele- 
mentary schools such facts only should be taught as can 
be verified either by the experience of the pupils or by 
the simplest experiments, which the pupils can repeat by 



8± THE ELEMENTARY TEACHING OF PHYSICAL SCIENCE. 

themselves ; and now, after this discussion, I add, that the 
teacher must depend on his own ingenuity for his exper- 
iments, and on his intercourse with his pupils for his in- 
struction. 

But you will tell me all this involves grave difficulties, 
and conditions incompatible with our ordinary school life. 
I freely admit the difficulties, but I am none the less sure 
that, unless science can be taught on the principles I have 
endeavored to illustrate, it had better not be taught at 
all. I know very well that the proper teaching of phys- 
ical science is wholly incompatible with our usual school 
methods. But this only proves to me that these methods 
ought to be changed, and I am persuaded that the 
changes required will benefit the literary and classical as 
well as the scientific courses of study. For do not the 
same general principles apply to the acquisition of knowl- 
edge in all subjects ? And when a child's perceptive facul- 
ties have been duly stimulated, and his intelligence fully 
awakened, he will find interest in grammar, in literature, 
or in history, as well as in science. 

In repelling the reproach of narrowness, to which our 
elective system at Cambridge undoubtedly frequently 
leads, how often have I urged the self-evident proposition 
that to arouse a love of study in any subject, I care not 
how subordinate its importance or how limited its scope, 
is to take the first step toward making your man a scholar ; 



THE TKUE TEACHER. 85 

while to fail to gain his interest in any study is to lose 
the whole end of education — and what is true of the man 
is still more true of the child. Classical culture on the 
one hand and scientific culture on the other are excellent 
things, but, if your boy can not be made to take an inter- 
est either in classics or in science, how plain it is that 
such treasures are not for him, and, in the absence of the 
one condition which can give value to any study, how 
idle and inconsequent all questions in regard to the rela- 
tive merits of these studies appear ! On the other hand, 
a love of study once gaiued, all studies are alike good. 

And as with the pupil, so with the teacher. No 
teaching is of any real value that does not come directly 
from the intelligence and heart of the teacher, and thus 
appeals to the intelligence and heart of the pupil. It, 
of course, implies more acquisition, and it requires far 
more energy to teach from one's own knowledge than to 
teach from a book, but then, just in proportion to the 
difficulties overcome, does the teacher raise his profession 
and ennoble himself. There is no nobler service than the 
life of -a true teacher ; but the mere task-master has no 
right to the teacher's name, and can never attain the 
teacher's reward. 



IV. 

THE KADIOMETEE: 

A FKESH EVIDENCE OF A MOLECULAR UNIVERSE. 

A Lecture delivered in the Sanders Theatre of Harvard University ', 
March 6, 1878. 

No one who is not familiar with the history of physi- 
cal science can appreciate how very modern are those 
grand conceptions which add so mnch to the loftiness of 
scientific studies ; and, of the many who, on one of our 
starlit nights, look up into the depths of space, and are 
awed by the thoughts of that immensity which come 
crowding upon the mind, there are few, I imagine, who 
realize the fact that almost all the knowledge which 
gives such great sublimity to that sight is the result of 
comparatively recent scientific investigation ; and that 
the most elementary student can now gain conceptions of 
the immensity of the universe of which the fathers of 
astronomy never dreamed. And how very grand are 



CELESTIAL MAGNITUDES. 87 

the familiar astronomical facts which the sight of the 
starry heavens suggests ! 

Those brilliant points are all suns like the one which 
forms the center of our system, and around which our 
earth revolves; yet so inconceivably remote, that, al- 
though moving through space with an incredible ve- 
locity, they have not materially changed their relative 
position since recorded observations began. Compared 
with their distance, the distance of our own sun — 92,000,- 
000 miles — seems as nothing; yet how inconceivable 
even that distance is when we endeavor to mete it out 
with our terrestrial standards ! For if, when Copernicus 
— the great father of modern astronomy — died, in 1543, 
just at the close of the Protestant Reformation, a mes- 
senger had started for the sun, and traveled ever since 
with the velocity of a railroad train — thirty miles an hour 
— he would not yet have reached his destination ! 

Evidently, then, no. standards, which, like our ordi- 
nary measures, bear a simple or at least a conceivable 
relation to the dimensions of our own bodies, can help us 
to stretch a line in such a universe. We must seek for 
some magnitude which is commensurate with these im- 
mensities of space ; and, in the wonderfully rapid motion 
of light, astronomy furnishes us with a suitable standard. 
By the eclipses of Jupiter's satellites the astronomers 
have determined that this mysterious effluence reaches us 



88 THE RADIOMETER. 

from the sun in eight minutes and a half, and therefore 
must travel through space with the incredible velocity- 
shall I dare to name it? — of 186,000 miles in a second of 
time ! Yet, inconceivably rapid as this motion is, capable 
of girdling the earth nearly eight times in a single sec- 
ond, the very nearest of the fixed stars, a Centauri, is so 
remote that the light by which it will be seen in the 
southern heavens to-night, near that magnificent con- 
stellation, the Southern Cross, must have started on its 
journey three years and a half ago. But this light comes 
from merely the threshold of the stellar universe ; and 
the telescope reveals to us stars so distant that, had they 
been blotted out of existence when history began, the 
tidings of the event could not yet have reached the earth ! 
Compare now with these grand conceptions the popu- 
lar belief of only a few centuries back. Where we look 
into the infinite depths, our Puritan forefathers saw 
only a solid dome hemming in the earth and skies, and 
through whose opened doors the rain descended. They 
regarded the sun and moon merely as great luminaries 
set in this firmament to rule the day and night, and to 
their understandings the stars served no better purpose 
than the spangles which glitter on the azure ceiling of 
many a modern church. The great work of Coperni- 
cus, " De Orbium Coelestium Revolutionibus," which was 
destined, ultimately, to overthrow the crude cosmography 



GROWTH OF SCIENTIFIC IDEAS. 89 

which Christianity had inherited from Judaism, was not 
published until just at the close of the author's life in 
1543, the date before mentioned. The telescope, which 
was required to fully convince the world of its previous 
error, was not invented until more than half a century 
later, and it was not until 1835 that Struve detected the 
parallax of a Lyrse. The measurement of this parallax, 
together with Bessel's determination of the parallax of 
61 Cygni, and Henderson's that of a Centauri, at about 
the same time, gave us our first accurate knowledge of 
the distances of the fixed stars. 

To the thought I have endeavored to express, I must 
add another, before I can draw the lesson which I wish 
to teach. Great scientific truths become popularized 
very slowly, and, after they have been thoroughly 
worked out by the investigators, it is often many years 
before they become a part of the current knowledge of 
mankind. It was fully a century after Copernicus died, 
with his great volume— still wet from the press of Nu- 
remberg — in his hands, before the Copernican theory 
was generally accepted even by the learned ; and the in- 
tolerant spirit with which this work was received and 
the persecution which Galileo encountered more than 
half a century later were due solely to the circumstance 
that the new theory tended to subvert the popular faith 
in the cosmography of the Church. In modern times, 



90 THE RADIOMETER. 

with the many popular expositors of science, the diffu- 
sion of new truth is more rapid ; but even now there 
is always a long interval after any great discovery 
in abstract science before the new conception is trans- 
lated into the language of common life, so that it 
can be apprehended by the mass even of educated 
men. 

I have thus dwelt on what must be familiar facts in 
the past history of astronomy, because they illustrate 
and will help you to realize the present condition of a 
much younger branch of physical science ; for, in the 
transition period I have described, there exists now a 
conception which opens a vision into the microcosmos 
beneath us as extensive and as grand as that which 
the Copernican theory revealed into the macrocosmos 
above us. 

The conception to which I refer will be at once sug- 
gested to every scientific scholar by the word molecule. 
This word is a Latin diminutive, which means, primarily, 
a small mass of matter ; and, although heretofore often 
applied in mechanics to the indefinitely small particles 
of a body between which the attractive or repulsive 
forces might be supposed to act, it has only recently 
acquired the exact significance with which we now 
use it. 

In attempting to discover the original usage of the 



BUFFON'S MOLECULES. 91 

word molecule, I was surprised to find that it was appar- 
ently first introduced into science by the great French 
naturalist, Buffon, who employed the term in a very 
peculiar sense. Buffon does not seem to have been trou- 
bled with the problem which so engrosses our modern 
naturalists — how the vegetable and animal kingdoms 
were developed into their present condition — bat he was 
greatly exercised by an equally difficult problem, which 
seems to have been lost sight of in the present contro- 
versy, and which is just as obscure to-day as it was in 
Buffon's time, at the close of the last century, and that 
is, Why species are so persistent in Nature; why the 
acorn always grows into the oak, and why every creature 
always produces of its kind. And, if you will reflect 
upon it, I am sure you will conclude that this last is by 
far the more fundamental problem of the two, and one 
which necessarily includes the first. That, of two eggs, 
in which no anatomist can discover any structural differ- 
ence, the one should, in a few short years, develop an in- 
telligence like Newton's, while the other soon ends in a 
Guinea-pig, is certainly a greater mystery than that, in 
the course of unnumbered ages, monkeys, by insensible 
gradations, should grow into men. 

In order to explain the remarkable constancy of spe- 
cies, Buffon advanced a theory which, when freed from 

a good deal that was fanciful, may be expressed thus : 

7 



92 THE RADIOMETER. 

The attributes of every species, whether of plants or of 
animals, reside in their ultimate particles, or, to use a 
more philosophical but less familiar word, inhere in these 
particles, which Buff on names organic molecules. Ac- 
cording to Buffon, the oak owes all the peculiarities of 
its organization to the special oak molecules of which it 
consists ; and so all the differences in the vegetable or 
animal kingdom, from the lowest to the highest species, 
depend on fundamental peculiarities with which their 
respective molecules were primarily endowed. There 
must, of course, be as many kinds of molecules as there 
are different species of living beings; but, while the 
molecules of the same species were supposed to be exact- 
ly alike, and to have a strong affinity or attraction for 
each other, those of different species were assumed to be 
inherently distinct and to have no such affinities. Buffon 
further assumed that these molecules of organic nature 
were diffused more or less widely through the atmos- 
phere and through the soil, and that the acorn grew to 
the oak simply because, consisting itself of oak molecules, 
it could draw only oak molecules from the surrounding 
media. 

With our present knowledge of the chemical consti- 
tution of organic beings, we can find a great deal that is 
both fantastic and absurd in this theory of Buffon ; but 
it must be remembered that the science of chemistry is 



WHAT IS A MOLECULE ? 93 

almost wholly a growth of the present century, while 
Buffon died in 1788 ; and, if we look at the theory solely 
from the standpoint of his knowledge, we shall find in it 
much that was worthy of this great man. Indeed, in our 
time, the essential features of the theory of Buffon have 
been transferred from natural history to chemistry al- 
most unchanged. 

According to our modern chemistry, the qualities of 
every substance reside or inhere in its molecules. Take 
this lump of sugar. It has certain qualities with which 
every one is familiar. Are those qualities attributes of 
the lump or of its parts? Certainly of its parts; for, 
if we break up the lump, the smallest particles will still 
taste sweet and show all* the characteristics of sugar. 
Could we, then, carry on this subdivision indefinitely, 
provided only we had senses or tests delicate enough to 
recognize the qualities of sugar in the resulting particles ? 
To this question, modern chemistry answers decidedly, 
~No ! You would before long reach the smallest mass 
that can have the qualities of sugar. You would have 
no difficulty in breaking up these masses, but you would 
then obtain, not smaller particles . of sugar, but particles 
of those utterly different substances which we call car- 
bon, oxygen, and hydrogen — in a word, particles of the 
elementary substances of which sugar consists. These 
ultimate particles of sugar we call the molecules of sugar, 



94 THE RADIOMETER. 

and thus we come to the present chemical definition of a 
molecule, " The smallest particles of a substance in which 
its qualities inhere" which, as you see, is a reproduction 
of Buff on- s idea, although applied to matter and not to 
organism. 

A lump of sugar, then, has its peculiar qualities be- 
cause it is an aggregate of molecules which have those 
qualities, and a lump of salt differs from a lump of sugar 
simply because the molecules of salt differ from those of 
sugar, and so with every other substance. There are as 
many kinds of molecules in Nature as there are different 
substances, but all the molecules of the same substance 
are absolutely alike in every respect. 

Thus far, as you see, we are merely reviving in a dif- 
ferent association the old ideas of Buff on. But just at 
this point comes in a new conception, which gives far 
greater grandeur to our modern theory : for we conceive 
that those smallest particles in which the qualities of a 
substance inhere are definite bodies or systems of bodies 
moving in space, and that a lump of sugar is a universe 
of moving worlds. 

If on a clear night you direct a telescope to one of 
the many star-clusters of our northern heavens, you will 
have presented to the eye as good a diagram as we can at 
present draw of what we suppose would, under certain 
circumstances, be seen in a lump of sugar if we could 



THE IDEA NOT ABSURD. 95 

look into the molecular universe with the same facility 
with which the telescope penetrates the depths of space. 

Do you tell me that the absurdities of Buffon were wis- 
dom when compared with such wild speculations as these ? 
The criticism is simply what I expected, and I must re- 
mind you that, as I intimated at the outset, this concep- 
tion of modern science is in the transition period of 
which I then spoke, and, although very familiar to scien- 
tific scholars, has not yet been grasped by the popular 
mind. I can further only add that, wild as it may 
appear, the idea is the growth of legitimate scientific 
investigation, and express my conviction that it will soon 
become as much a part of the popular belief as those 
grand conceptions of astronomy to which I have re- 
ferred. 

Do you rejoin that we can see the suns in a stellar clus- 
ter, but can not even begin to see the molecules ? I must 
again remind you that, in fact, you only see points of 
light in the field of the telescope, and that your knowl- 
edge that these points are immensely distant suns is an 
inference of astronomical science ; and, further, that our 
knowledge — if I may so call our confident belief — that 
the lump of sugar is an aggregate of moving molecules 
is an equally legitimate inference of molecular mechan- 
ics, a science which, although so much newer, is as posi- 
tive a field of study as astronomy. Moreover, sight is 



96 THE RADIOMETER. 

not the only avenue to knowledge; and, although our 
material limitations forbid us to expect that the micro- 
scope will ever be able to penetrate the molecular uni- 
verse, yet we feel assured that we have been able by 
strictly experimental methods to weigh molecular masses 
and measure molecular magnitudes with as much accu- 
racy as those of the fixed stars. 

Of all forms of matter the gas has the simplest mo- 
lecular structure, and, as might be anticipated, our knowl- 
edge of molecular magnitudes is as yet chiefly confined 
to materials of this class. I have given below some of 
the results which have been obtained in regard to the 
molecular magnitudes of hydrogen gas, one of the best 
studied of this class of substances ; and, although the vast 
numbers are as inconceivable as are those of astronomy, 
they can not fail to impress you with the reality of the 
magnitudes they represent. I take hydrogen gas for my 
illustration rather than air, because our atmosphere is a 
mixture of two gases, oxygen and nitrogen, and therefore 
its condition is less simple than that of a perfectly 
homogeneous material like hydrogen. The molecular 
dimensions of other substances, although varying very 
greatly in their relative values, are of the same order 
of magnitude as these.* 

* As some of the readers of this volume may be interested to compare 
these values, we reproduce the "Table of Molecular Data" from Professor 



DIMENSIONS OF MOLECULES. 



97 



Dimensions of Hydrogen Molecules calculated for lemperature of 
Melting Ice, and for the Mean Height of the Barometer of the 
Sea Level : 

Mean velocity, 6,099 feet a second. 

Mean path, 31 ten-inillionths of an inch. 

Collisions, 17,750 millions each second. 

Diameter, 438,000, side by side, measure y-J^ of an inch. 

Mass, 14 (millions 3 ) weigh j-^ of a grain. 

Gas- volume, 311 (millions 3 ) fill one cubic inch. 

To explain how the values here presented were 
obtained would be out of place in a popular lec- 

Clerk Maxwell's lecture on u Molecules," delivered before the British Asso- 
ciation at Bradford, and published in "Nature," September 25, 1SV3. 



Molecular Magnitudes at Standard Temperature and Pressure, 0° C. and 

76 c. m. 



RANK ACCORDING TO ACCURACY OF KNOWL- 
EDGE. 



Rank I. 

Relative mass 

Velocity in metres per second 

Rank II. 

Mean path in ten billionths (, -10 ) °f a metre. 
Collisions each second — number of millions 



Rank III. 

Diameter in hundred billionths do- 11 ) of a metre. . 

Mass in ten million million million millionths ( 10 - as 

of a gramme 



Hydrogen. Oxyg«n 



1 

1,S59 



9G5 
17,750 



58 



16 
465 



5eo 

7,646 



76 

736 



Carbonic Carbonic 
Oxide. Dioaide. 



14 

497 



482 
9,489 



83 
644 



22 



379 



93 
1,012 



Number of molecules in one cubic centimetre of every gas is nineteen 
million million million on 19 (, o 1 8 ). 

Two million hydrogen molecules side by side measure a little over one 
millimetre. 



98 THE RADIOMETER. 

tare,* but a few words in regard to two or three of 
the data are required to elucidate the subject of this 
lecture. 

First, then, in regard to the mass or weight of the 
molecules. So far as their relative values are concerned, 
chemistry gives us the means of determining the mo- 
lecular weights with very great accuracy ; but when we 
attempt to estimate their weights in fractions of a grain 
— the smallest of our common standards — we can not 
expect precision, simply because the magnitudes com- 
pared are of such a different order ; and the same is true 
of most of the other absolute dimensions, such as the 
diameter and volume of the molecules. We only regard 
the values given in our table as a very rough estimate, 
but still we have good grounds for believing that they 
are sufficiently accurate to give us a true idea of the order 
of the quantities with which, we are dealing ; and it will 
be seen that, although the numbers required to express 
the relations to our ordinary standards are so large, these 
molecular magnitudes are no more removed from us on 
the one side than are those of astronomy on the other. 

Passing next to the velocity of the molecular motion, 
we find in that a quantity which, although large, is com- 
mensurate with the velocity of sound, the velocity of a 

* See Professor Maxwell's lecture, he. cit. ; also, Appletons' " Cyclopae- 
dia " article " Molecules." 



VELOCITY OP MOLECULES. 99 

rifle -ball, and the velocities of many other motions with 
which we are familiar. "We are, therefore, not com- 
paring, as before, quantities of an utterly different order, 
and we have confidence that we have been able to deter- 
mine the value within very narrow limits of error. But 
how surprising the result is ! Those molecules of hydro- 
gen are constantly moving to and fro with this great 
velocity, and not only are the molecules of all aeri- 
form substances moving at similar, although differing 
rates, but the same is equally true of the molecules 
of every substance, whatever may be its state of aggre- 
gation. 

The gas is the simplest molecular condition of matter, 
because in this state the molecules are so far separated 
from each other that their motions are not influenced by 
mutual attractions. Hence, in accordance with the well- 
known laws of motion, gas molecules must always move 
in straight lines and with a constant velocity until they 
collide with each other or strike against the walls of the 
containing vessel, when, in consequence of their elasticity, 
they at once rebound and start on a new path with a new 
velocity. In these collisions, however, there is no loss of 
motion, for, as the molecules have the same weight and 
are perfectly elastic, they simply change velocities, and 
whatever one may lose the other must gain. 

But, if the velocity changes in this way, you may ask, 



100 THE RADIOMETER. 

What meaning has the definite value given in our table I 
The answer is, that this is the mean value of the velocity 
of all the molecules in a mass of hydrogen gas under the 
assumed conditions; and, by the principle just stated, 
the mean value can not be changed by the collisions of 
the molecules among themselves, however great may be 
the change in the motion of the individuals. 

In both liquids and solids the molecular motions are 
undoubtedly as active as in a gas, but they must be greatly 
influenced by the mutual attractions which hold the par- 
ticles together, and hence the conditions are far more 
complicated, and present a problem which we have been 
able to solve only very imperfectly, and with which, 
fortunately, we have not at present to deal. 

Limiting, then, our study to the molecular condition 
of a gas, picture to yourselves what must be the condition 
of our atmosphere, with its molecules flying about in all 
directions. Conceive what a molecular storm must be 
raging about us, and how it must beat against our bodies 
and against every exposed surface. The molecules of 
our atmosphere move, on an average, nearly four (3*8) 
times slower than those of hydrogen under the same con- 
ditions ; but then they weigh, on an average, fourteen 
and a half times more than hydrogen molecules, and 
therefore strike with as great energy. And do not think 
that the effect of these blows is insignificant because the 



MOVING POWER OF MOLECULES. 101 

molecular projectiles are so small ; they make up by 
their number for what they want in size. 

Consider, for example, a cubic yard of air, which, if 
measured at the freezing-point, weighs considerably over 
two pounds. That cubic yard of material contains over 
two pounds of molecules, which are moving with an 
average velocity of 1,605 feet a second, and this motion 
is equivalent, in every respect, to that of a cannon-ball of 
equal weight rushing along its path at the same tre- 
mendous rate. Of course, this is true of every cubic 
yard of air at the same temperature ; and, if the motion 
of the molecules of the atmosphere around us could by 
any means be turned into one and the same direction, 
the result would be a hurricane sweeping over the earth 
with this velocity — that is, at the rate of 1,094 miles an 
hour — whose destructive violence not even the Pyramids 
could withstand. 

Living as we do in the midst of a molecular torna- 
do capable of such effects, our safety lies wholly in 
the circumstance that the storm beats equally in all 
directions at the same time, and the force is thus so 
exactly balanced that we are wholly unconscious of the 
tumult. Not even the aspen-leaf is stirred, nor the 
most delicate membrane broken ; but let us remove 
the air from one of the surfaces of such a mem- 
brane, and then the power of the molecular storm be- 



102 THE RADIOMETER. 

comes evident, as in the familiar experiments with an 
air-pump. 

As lias already been intimated, the values of the velo- 
cities both of hydrogen and of air molecules given above 
were measured at a definite temperature, 32° of our 
Fahrenheit thermometer, the freezing-point of water; 
and this introduces a very important point bearing on our 
subject, namely, that the molecular velocities vary very 
greatly with the temperature. Indeed, according to our 
theory, this very molecular motion constitutes that state 
or condition of matter which we call temperature. A 
hot body is one whose molecules are moving compara- 
tively rapidly, and a cold body one in which they are 
moving comparatively slowly. Without, however, enter- 
ing into further details, which would involve the whole 
mechanical theory of heat, let me call your attention to a 
single consequence of the principle I have stated. 

When we heat hydrogen, air, or any mass of gas, we 
simply increase the velocity of its moving molecules. 
When we cool the gas, we simply lessen the velocity of 
the same molecules. Take a current of air which enters 
a room through a furnace. In passing it comes in con- 
tact with heated iron, and, as we say, is heated. But, as 
we view the process, the molecules of the air, while in 
contact with the hot iron, collide with the very rapidly 
oscillating metallic molecules, and fly back as a billiard- 



EFFECT OF RECOIL. 103 

ball would under similar circumstances, with a greatly 
increased velocity, and it is this more rapid motion which 
alone constitutes the higher temperature. 

Consider, next, what must be the effect on the sur- 
face. A moment's reflection will show that the normal 
pressure exerted by the molecular storm, always raging 
in the atmosphere, is due not only to the impact of the 
molecules, but also to the reaction caused by their re- 
bound. When the molecules rebound, they are, as it 
were, driven away from the surface in virtue of the in- 
herent elasticity both of the surface and of the mole- 
cules. Now, what takes place when one mass of matter 
is driven away from another — when a cannon-ball is 
driven out of a gun, for example ? Why, the gun kicks ! 
And so every surface from which molecules rebound 
must kick; and, if the velocity is not changed by the 
collision, one half of the pressure caused by the molecu- 
lar bombardment is due to the recoil. From a heated 
surface, as we have said, the molecules rebound with an 
increased velocity, and hence the recoil must be propor- 
tionally increased, determining a greater pressure against 
the surface. 

According to this theory, then, we should expect that 
the air would press unequally against surfaces at different 
temperatures, and that, other things being equal, the 
pressure exerted would be greater the higher the tern- 



101 THE RADIOMETER. 

perature of the surface. Such a result, of course, is 
wholly contrary to common experience, which tells us 
that a uniform mass of air presses equally in all direc- 
tions and against all Surfaces of the same area, whatever 
may be their condition. It would seem, then, at first 
sight, as if we had here met with a conspicuous case in 
which our theory fails. But further study will convince 
us that the result is just what we should expect in a 
dense atmosphere like that in which we dwell ; and, in 
order that this may become evident, let me next call 
your attention to another class of molecular magnitudes. 

It must seem strange indeed that we should be able 
to measure molecular velocities; but the next point I 
have to bring to your notice is stranger yet, for we are 
confident that we have been able to determine with ap- 
proximate accuracy for each kind of gas molecule the 
average number of times one of these little bodies runs 
against its neighbors in a second, assuming, of course, 
that the conditions of the gas are given. Knowing, now, 
the molecular velocity and the number of collisions a 
second, we can readily calculate the mean path of the 
molecule — that is, the average distance it moves, under 
the same conditions, between two successive collisions. 
Of course, for any one molecule, this path must be con- 
stantly varying; since, while at one time the molecule 
may find a clear coast and make a long run, the very 



RATE OF DIFFUSION. 105 

next time it may hardly start before its course is arrested. 
Still, taking a mass of gas under constant conditions, the 
doctrine of averages shows that the mean path must 
have a definite value, and an illustration will give an 
idea of the manner in which we have been able to esti- 
mate it. 

The nauseous, smelling gas we call sulphide of hydro- 
gen has a density only a little greater than that of air, 
and its molecules must therefore move with very nearly 
as great velocity as the average air molecule — that is to 
say, about fourteen hundred and eighty feet a second ; 
and we might therefore expect that, on opening a jar of 
the gas, its molecules would spread instantly through the 
surrounding atmosphere. But, so far from this, if the 
air is quiet, so that the gas is not transported by currents, 
a very considerable time will elapse before the character- 
istic odor is perceived on the opposite side of an ordinary 
room. The reason is obvious : the molecules must elbow 
their way through the crowd of air molecules which al- 
ready occupy the space, and can therefore advance only 
slowly ; and it is obvious that, the of tener they come into 
collision with their neighbors, the slower their progress 
must be. Knowing, then, the mean velocity of the 
molecular motion, and being able to measure by appro- 
priate means the rate of diffusion, as it is called, we have 
the data from which we can calculate both the number 



106 THE KADIOMETER. 

of collisions in a second and also the mean path between 
two successive collisions. The results, as we must expect, 
are of the same order as the other molecular magnitudes. 
But, inconceivably short as the free * path of a molecule 
certainly is, it is still, in the case of hydrogen gas, 136 
times the diameter of the moving body, which would 
certainly be regarded among men as quite ample elbow- 
room. 

Although, in this lecture, I have as yet had no occa- 
sion to mention the radiometer, I have by no means for- 
gotten my main subject, and everything which has been 
said has had a direct bearing on the theory of this re- 
markable instrument; and still, before you can under- 
stand the great interest with which it is regarded, we 
must follow out another line of thought, converging on 
the same point. 

One of the most remarkable results of modern science 
is the discovery that all energy at work on the surface of 
this planet comes from the sun. Most of you probably 
saw, at our Centennial Exhibition, that great artificial 
cascade in Machinery Hall, and were impressed with the 

* There is an obvious distinction between the free and the disturbed 
path of a molecule, and we can not overlook in our calculations the pertur- 
bations which the collisions necessarily entail. Such considerations greatly 
complicate the problem, which is far more difficult than would appear from 
the superficial view of the subject that can alone be given in a popular 
lecture. 



POWER COMES FROM THE SUN. 107 

power of the steam-pump which could keep flowing such 
a mass of water. But, also, when you stood before the 
falls at Niagara, did you realize the fact that the enor- 
mous floods of water which you saw surging over those 
cliffs were in like manner supplied by an all-powerful 
pump, and that pump the sun? And not only is this 
true, but it is equally true that every drop of water that 
falls, every wave that beats, every wind that blows, every 
creature that moves on the surface of the earth, one and 
all, are animated by that mysterious effluence we call 
the sunbeam. I say mysterious effluence ; for how that 
power is transmitted over those 92,000,000 miles between 
the earth and the sun is still one of the greatest myste- 
ries of Nature. 

In the science of optics, as is well known, the phe- 
nomena of light are explained by the assumption that 
the energy is transmitted in waves through a medium 
which fills all space called the luminiferous ether, and 
there is no question that this theory of Nature, known 
in science as the Undulatory Theory of Light, is, as a 
working hypothesis, one of the most comprehensive and 
searching which the human mind has ever framed. It 
has both correlated known facts and pointed the way to 
remarkable discoveries. But, the moment we attempt to 
apply it to the problem before us, it demands conditions 
which tax even a philosopher's credulity. 



108 THE RADIOMETER. 

As sad experience on the ocean only too frequently 
teaches, energy can be transmitted by waves as well as 
in any other way. But every mechanic will tell you 
that the transmission of energy, whatever be the means 
employed, implies certain well-known conditions. As- 
sume that the energy is to be used to turn the spindles of 
a cotton mill. The engineer can tell you just how many 
horse-power he must supply for every working-day, and 
it is equally true that a definite amount of energy must 
come from the sun to do each day's work on the surface 
of the globe. Further, the engineer will also tell you 
that, in order to transmit the power from his turbine or 
his steam-engine, he must have shafts and pulleys and 
belts of adequate strength, and he knows in every case 
what is the lowest limit of safety. In like manner, the 
medium through which the energy which runs the world 
is transmitted must be strong enough to do the immense 
work put upon it ; and, if the energy is transmitted by 
waves, this implies that the medium must have an enor- 
mously great elasticity, an elasticity vastly greater than 
that of the best-tempered steel. 

But turn now to the astronomers, and learn what they 
have to tell us in regard to the assumed luminiferous 
ether through which all this energy is supposed to be 
transmitted. Our planet is rushing in its orbit around 
the sun at an average rate of over 1,000 miles a minute, 



HOW TRANSMITTED. 109 

and makes its annual journey of some 550,000,000 miles 
in 365 days, 6 hours, 9 seconds, and ^ of a second. Mark 
the tenths; for astronomical observations are so accurate 
that, if the length of the year varied permanently by 
the tenth of a second, we should know it ; and you can 
readily understand that, if there were a medium in space 
which offered as much resistance to the motion of the 
earth as would gossamer threads to a race-horse, the 
planet could never come up to time, year after year, to 
the tenth of a second. 

How, then, can we save our theory by which we set 
so much, and rightly, because it has helped us so effec- 
tively in studying Nature ? If we may be allowed such 
an extravagant solecism, let us suppose that the engineer 
of our previous illustration was the hero of a fairy tale. 
He has built a mill, set a steam-engine in the basement, 
arranged his spindles above, and is connecting the pulleys 
by the usual belts, when some stern necessity requires 
him to transmit all the energy with cobwebs. Of course, 
a good fairy comes to his aid, and what does she do ? 
Simply makes the cobwebs indefinitely strong. So 
the physicists, not to be outdone by any fairies, make 
their ether indefinitely elastic, and their theory lands 
them just here, with a medium filling all space, thou- 
sands of times more elastic than steel, and thousands on 
thousands of times less dense than hydrogen gas. There 



HO THE KADIOHETER. 

must be a fallacy somewhere, and I strongly suspect it 
is to be found in our ordinary materialistic notions of 
causation, winch involve the old metaphysical dogma, 
"nulla actio in distans" and which in our day have 
culminated in the famous apothegm of the German 
materialist, " Kein Phosphor kein Gredanke." 

But it is not my purpose to discuss the doctrines of 
causation, and I have dwelt on the difficulty, which this 
subject presents in connection with the undulatory the- 
ory, solely because I wished you to appreciate the great 
interest with which scientific men have looked for some 
direct manifestation of the mechanical action of light. It 
is true that the ether waves must have dimensions similar 
to those of the molecules discussed above, and we must 
expect, therefore, that they would act primarily on the 
molecules and not on masses of matter. But still the 
well-known principles of wave motion have led compe- 
tent physicists to maintain that a more or less consider- 
able pressure ought to be exerted by the ether waves on 
the surfaces against which they beat, as a partial resultant 
of the molecular tremors first imparted. Already, in the 
last century, attempts were made to discover some evi- 
dence of such action, and in various experiments the 
sun's direct rays were concentrated on films, delicately 
suspended and carefully protected from all other extrane- 
ous influences, but without any apparent effect ; and thus 



DESCRIPTION OF INSTRUMENT. m 

the question remained until about three years ago, when 
the scientific world were startled by the announcement 
of Mr. Crookes, of London, that, on suspending a small 
piece of blackened alder pith in the very perfect vacuum 
which can now be obtained with the mercury pump, in- 
vented by Sprengel, he had seen this light body actually 
repelled by the sun's rays ; and they were still more star- 
tled, when, after a few further experiments, he presented 
us with the instrument he called a radiometer, in which 
the sun's rays do the no inconsiderable work of turning 
a small wheel. Let us examine for a moment the con- 
struction of this remarkable instrument. 

The moving part of the radiometer is a small hori- 
zontal wheel, to the ends of whose arms are fastened 
vertical vanes, usually of mica, and blackened on one 
side. A glass cap forms the hub, and by the glass- 
blower's art the wheel is inclosed in a glass bulb, so that 
the cap rests on the point of a cambric needle ; and the 
wheel is so delicately balanced on this pivot that it turns 
with the greatest freedom. From the interior of the 
bulb the air is now exhausted by means of the Sprengel 
pump, until less than g o0 of the original quantity is 
left, and the only opening is then hermetically sealed. 
If, now, the sun's light or even the light from a candle 
shines on the vanes, the blackened surfaces — which are 
coated with lampblack — are repelled, and, these being 



112 THE RADIOMETER. 

symmetrically placed around the wheel, the several forces 
conspire to produce the rapid motion which results. The 
effect has all the appearance of a direct mechanical action 
exerted by the light, and for some time was so regarded 
by Mr. Crookes and other eminent physicists, although 
in his published papers it should be added that Mr. 
Crookes carefully abstained from speculating on the 
subject — aiming, as he has since said, to keep himself 
unbiased by any theory, while he accumulated the facts 
upon which a satisfactory explanation might be based. 

Singularly, however, the first aspects of the new phe- 
nomena proved to be wholly deceptive, and the motion, 
so far from being an effect of the direct mechanical 
action of the waves of light, is now believed to be a new 
and very striking manifestation of molecular motion. To 
this opinion Mr. Crookes himself has come, and, in a re- 
cent article, he writes : " Twelve months' research, how- 
ever, has thrown much light on these actions, and the 
explanation afforded by the dynamical theory of gases 
makes what was a year ago obscure and contradictory 
now reasonable and intelligible." 

As is frequently the case in Nature, the chief effect 
is here obscured by various subordinate phenomena, and 
it is not surprising that a great difference of opinion 
should have arisen in regard to the cause of the motion. 
This would not be an appropriate place to describe the 



DIFFERENCE OF OPINION. H3 

numerous investigations occasioned by the controversy, 
man j of which show in a most striking manner how easily 
experimental evidence may be honestly misinterpreted 
in support of a preconceived opinion. I will, however, 
venture to trespass further on your patience, so far as to 
describe the few experiments by which, very early in 
the controversy, I satisfied my own mind on the subject. 

When, two years ago, I had for the first time an op- 
portunity of experimenting with a radiometer, the opinion 
was still prevalent that the motion of the wheel was a 
direct mechanical effect of the waves of light, and, there- 
fore, that the impulses came from the outside of the in- 
strument, the waves passing freely through the glass 
envelope. At the outset, this opinion did not seem to 
me to be reasonable, or in harmony with well-known 
facts ; for, knowing how great must be the molecular 
disturbance caused by the sun's rays, as shown by their 
heating power, I could not believe that a residual action, 
such as has been referred to, would first appear in these 
delicate phenomena observed by Mr. Crookes, and should 
only be manifested in the vacuum of a mercury pump. 

On examining the instrument, my attention was at 
once arrested by the lampblack coating on the alternate 
surfaces of the vanes ; and, from the remarkable power 
of lampblack to absorb radiant heat, it was evident at 
once that, whatever other effects the rays from the sun 



114 THE RADIOMETER. 

or from a flame miglit cause, they must necessarily de- 
termine a constant difference of temperature between the 
two surfaces of the vanes, and the thought at once oc- 
curred that, after all, the motion might be a direct result 
of this difference of temperature — in other words, that 
the radiometer might be a small heat engine, whose mo- 
tions, like those of every other heat engine, depend on 
the difference of temperature between its parts. 

But, if this were true, the effect ought to be propor- 
tional solely to the heating power of the rays, and a very 
easy means of roughly testing this question was at hand. 
It is well known that an aqueous solution of alum, al- 
though transmitting light as freely as the purest water, 
powerfully absorbs those rays, of any source, which have 
the chief heating power. Accordingly, I interposed what 
we call an alum cell in the path of the rays shining 
on the radiometer, when, although the light on the vanes 
was as bright as before, the motion was almost completely 
arrested. 

This experiment, however, was not conclusive, as it 
might still be said that the heat-giving rays acted me- 
chanically, and it must be admitted that the chief part 
of the energy in the rays, even from the most brilliant 
luminous sources, always takes the form of heat. But, 
if the action is mechanical, the reaction must be against 
the medium through which the rays are transmitted, 



METHOD OF INVESTIGATION. H5 

while, if the radiometer is simply a heat engine, the action 
and reaction must be, ultimately at least, between the 
heater and the cooler, which in this case are respectively 
the blackened surfaces of the vanes and the glass walls of 
the inclosing bulb ; and here, again, a very easy method 
of testing the actual condition at once suggested itself. 

If the motion of the radiometer wheel is an effect of 
mechanical impulses transmitted in the direction of the 
beam of light, it was certainly to be expected that the 
beam would act on the lustrous as well as on the black- 
ened mica surfaces, however large might be the differ- 
ence in the resultants producing mechanical motion, in 
consequence of the great absorbing power of the lamp- 
black. Moreover, since the instrument is so constructed 
that, of two vanes on opposite sides of the wheel, one 
always presents a blackened and the other a lustrous sur- 
face to an incident beam, we should further expect to 
find in the motion of the wheel a differential phenom- 
enon, due to the unequal action of the light on these sur- 
faces. On the other hand, if the radiometer is a heat 
engine, and the reaction takes place between the heated 
blackened surfaces of the vanes and the colder glass, it is 
evident that the total effect will be simply the sum of 
the effects at the several surfaces. 

In order to investigate the question thus presented, I 
placed the radiometer before a common kerosene lamp, 



116 THE RADIOMETER. 

and observed, with a stop-watch, the number of seconds 
that elapsed during ten revolutions of the little wheel. 
Finding that this number was absolutely constant, I next 
screened one half of the bulb, so that only the blackened 
faces were exposed to the light as the wheel turned them 
into the beam. Again, I several times observed the 
number of seconds during ten turns, which, although 
equally constant, was greater than before. Lastly, I 
screened the blackened surfaces so that, as the wheel 
turned, only the lustrous surfaces of mica were exposed 
to the light, when, to my surprise, the wheel continued 
to turn in the same direction as before, although much 
more slowly. It appeared as if the lustrous surfaces 
were attracted by the light. Again I observed the time 
of ten revolutions, and here I have collected my results, 
reducing them, in the last column, so as to show the cor- 
responding number of revolutions in the same time : 



CONDITIONS. 


Time of ten revolu- 
tions. 


No. of revolutions in 
same time. 


Both faces exposed 


8 seconds. 
11 " 
29 " 


319 


Blackened faces only 


232 


Mica faces only 


88 







It will be noticed that 88 -f- 232 equals very nearly 
319. Evidently the effect, so far from being differen- 
tial, is concurrent. Hence, the action which causes the 
motion must take place between the parts of the instru- 



A HEAT ENGINE.' H7 

ment, and can not be a direct effect of impulses imparted 
by ether waves ; or else we are driven to the most im- 
probable alternative, that lampblack and mica should 
have such a remarkable selective power that the impulses 
imparted by the light should exert a repulsive force at 
one surface and an attractive force at the other. Were 
there, however, such an improbable effect, it must be 
independent of the thickness of the mica vanes ; while, 
on the other hand, if, as seemed to us now most probable, 
the whole effect depended on the difference of tempera- 
ture between the lampblack and the mica, and if the 
light produced an effect on the mica surface only be- 
cause, the mica plate being diathermous to a very con- 
siderable extent, the lampblack became heated through 
the plate more than the plate itself, then it would follow 
that, if we used a thicker mica plate, which would absorb 
more of the heat, we ought to obtain a marked differ- 
ence of effect. Accordingly, we repeated the experiment 
with an equally sensitive radiometer, which we made for 
the purpose, with comparatively thick vanes, and with 
this the effect of a beam of light on the mica surface was 
absolutely null, the wheel revolving in the same time, 
whether these faces were protected or not. 

But one thing was now wanting to make the demon- 
stration complete. A heat engine is reversible, and if 
the motion of the radiometer depended on the circum- 



118 THE RADIOMETER. 

stance that the temperature of the blackened faces of the 
vanes was higher than that of the glass, then by revers- 
ing the conditions we onght to reverse the motion. Ac- 
cordingly, I carefully heated the glass bulb over a lamp, 
until it was as hot as the hand would bear, and then 
placed the instrument in a cold room, trusting to the 
great radiating power of lampblack to maintain the tem- 
perature of the blackened surfaces of the vanes below 
that of the glass. Immediately the wheel began to turn 
in the opposite direction, and continued to turn until the 
temperature of the glass came into equilibrium with the 
surrounding objects. 

These early experiments have since been confirmed 
to the fullest extent, and no physicist at the present day 
can reasonably doubt that the radiometer is a very beau- 
tiful example of a heat engine, and it is the first that has 
been made to work continuously by the heat of the sun- 
beam. But it is one thing to show that the instrument 
is a heat engine, and quite another thing to explain in 
detail the manner in which it acts. In regard to the last 
point, there is still room for much difference of opinion, 
although physicists are generally agreed in referring the 
action to the residual gas that is left in the bulb. As 
for myself, I became strongly persuaded — after experi- 
menting with more than one hundred of these instru- 
ments, made under my own eye, with every variation of 



CAUSE OF MOTION. 119 

condition I could suggest — that the effect was due to the 
same cause which determines gas pressure, and, according 
to the dynamical theory of gases, this amounts to saying 
that the effect is due to molecular motion. I have not 
time, however, to describe either my own experiments on 
which this opinion was first based, or the far more thor- 
ough investigations since made by others, which have 
served to strengthen the first impression.* But, after 
our previous discussions, a few words will suffice to show 
how the molecular theory explains the new phenomena. 

Although the air in the bulb has been so nearly ex- 
hausted that less than the one-thousandth part remains, 
yet it must be borne in mind that the number of mole- 
cules left behind is by no means inconsiderable. As will 
be seen by referring to our table, there must still be no 
less than 311,000 million million in every cubic inch. 
Moreover, the absolute pressure which this residual gas 
exerts is a very appreciable quantity. It is simply the 
one-thousandth of the normal pressure of the atmosphere, 
that is, of I^y 7 ^ pounds on a square inch, which is equiv- 
alent to a little over one hundred grains on the same 
area. Now, the area of the blackened surfaces of the 
vanes of an ordinary radiometer measures just about a 
square inch, and the wheel is mounted so delicately that 

* See notice of these investigations by the author of this article, in 
"American Journal of Science and Arts," September, 1877 (3), xiv, 231. 



120 THE RADIOMETER. 

a constant pressure of one-tenth of a grain would be suf- 
ficient to produce rapid motion. So that a difference of 
pressure on the opposite faces of the vanes, equal to one 
one-thousandth of the whole amount, is all that we need 
account for ; and, as can easily be calculated, a difference 
of temperature of less than half a degree Fahrenheit 
would cause all this difference in the pressure of the 
rarefied air. 

But you may ask, How can such a difference of press- 
ure exist on different surfaces exposed to one and the 
same medium ? and your question is a perfectly legiti- 
mate one ; for it is just here that the new phenomena 
seem to belie all our previous experience. If, however, 
you followed me in my very partial exposition of the me- 
chanical theory of gases, you will easily see that on this 
theory it is a more difficult question to explain why such 
a difference of pressure does not manifest itself in every 
gas medium and under all conditions between any two 
surfaces having different temperatures. 

"We saw that gas pressure is a double effect, caused 
both by the impact of molecules and by the recoil of the 
surface attending their rebound. We also saw that when 
molecules strike a heated surface they rebound with in- 
creased velocity, and hence produce an increased pressure 
against the surface, the greater the higher the tempera- 
ture. According to this theory, then, we should expect 



WHY EXHAUST THE AIR? 121 

to find the same atmosphere pressing unequally on equal 
surfaces if at different temperatures ; and the difference 
in the pressure on the lampblack and mica surfaces of 
the vanes, which the motion of the radiometer wheel ne- 
cessarily implies, is therefore simply the normal effect of 
the mechanical condition of every gas medium. The 
real difficulty is, to explain why we must exhaust the air 
so perfectly before the effect manifests itself. 

The new theory is equal to the emergency. As has 
been already pointed out, in the ordinary state of the air 
the amplitude of the molecular motion is exceedingly 
small, not over a few ten-millionths of an inch — a very 
small fraction, therefore, of the height of the inequalities 
on the lampblack surfaces of the vanes of a radiometer. 
Under such circumstances, evidently the molecules would 
not leave the heated surface, but simply bound back and 
forth between the vanes and the surrounding mass of 
dense air, which, being almost absolutely a non-conductor 
of heat, must act essentially like an elastic solid wall con- 
fining the vanes on either side. For the time being, 
and until replaced by convection currents, the oscillating 
molecules are as much a part of the vanes as our atmos- 
phere is a part of the earth ; and on this system, as a 
whole, the homogeneous dense air which surrounds it 
must press equally from all directions. In proportion, 
however, as the air is exhausted, the molecules find more 



122 THE RADIOMETER. 

room and the amplitude of the molecular motion is in- 
creased, and, when a very high degree of exhaustion is 
reached, the air particles no longer bound back and forth 
on the yahes without change of condition, but they either 
bound off entirely like a ball from a cannon, or else, hav- 
ing transferred a portion of their momentum, return with 
diminished velocity, and in either case the force of the 
reaction is felt.* 

* The reader will, of course, distinguish between the differential action 
on the opposite faces of the vanes of the radiometer and the reaction be- 
tween the vanes and the glass which are the heater and the cooler of the 
little engine. Nor will it be necessary to remind any student that a popu- 
lar view of such a complex subject must be necessarily partial. In the 
present case we not only meet with the usual difficulties in this respect, but, 
moreover, the principles of molecular mechanics have not been so fully de- 
veloped as to preclude important differences of opinion between equally 
competent authorities in regard to the details of the theory. To avoid mis- 
apprehension, we may here add that, in order to obtain in the radiometer a 
reaction between the heater and the cooler, it is not necessary that the 
space between them should actually be crossed by the moving molecules. 
It is only necessary that the momentum should be transferred across the 
space, and this may take place along lines consisting of many molecules 
each. The theory, however, shows that such a transfer can only take place 
in a highly rarefied medium. In an atmosphere of ordinary density, the 
accession of heat which the vanes of a radiometer might receive from a 
radiant source would be diffused through the mass of the inclosed air. 
This amounts to saying that the momentum would be so diffused, and 
hence, under such circumstances, the molecular motion would not determine 
any reaction between the vanes and the glass envelope. Indeed, a dense 
mass of gas presents to the conduction of heat, which represents momen- 
tum, a wall far more impenetrable than the surrounding glass, and the dif- 
fusion of heat is almost wholly brought about by convection currents which 
rise from the heated surfaces. It will thus be seen that the great non-con- 



CONCLUSIONS REACHED. 123 

Thus it appears that we have been able to show by 
very definite experimental evidence that the radiometer 
is a heat engine. We have also been able to show that 
such a difference of temperature as the radiation must 
produce in the air in direct contact with the opposite 
faces of the vanes of the radiometer would determine a 
difference of tension, which is sufficient to account for 
the motion of the wheel. Finally, we have shown, as 
fully as is possible in a popular lecture, that, according to 
the mechanical theory of gases, such a difference of ten- 
sion would have its normal effect only in a highly rare- 
fied atmosphere, and thus we have brought the new 
phenomena into harmony with the general principles of 
molecular mechanics previously established. 

More than this can not be said of the steam-engine, 
although, of course, in the older engine the measure- 
ducting power of air comes into play to prevent not only the transfer of 
momentum from the vanes to the glass, but also, almost entirely, any direct 
transfer to the surrounding mass of gas. ITence, as stated above, the heat- 
ed molecules bound back and forth on the vanes without change of condi- 
tion, and the mass of the air retains its uniform tension in all parts of the 
bulb, except in so far as this is slowly altered by the convection currents 
just referred to. As the atmosphere, however, becomes less dense, the dif- 
fusion of heat by convection diminishes, and that by molecular motion (con- 
duction) increases until the last greatly predominates. When, now, the 
exhaustion reaches so great a degree that the heat, or momentum, is rap- 
idly transferred from the heater to the cooler by an exaggeration, or, pos- 
sibly, a modification, of the mode of action we call conduction, then we have 
the reaction on which the motion of the radiometer wheel depends. 
9 



124 THE RADIOMETER. 

ments on which the theory is based are vastly more accu- 
rate and complete. But the moment we attempt to go 
beyond the general principles of heat engines, of which 
the steam-engine is such a conspicuous illustration, and 
explain how the heat is transformed into motion, we 
have to resort to the molecular theory just as in the case 
of the radiometer ; and the motion of the steam-engine 
seems to us less wonderful than that of the radiometer 
only because it is more familiar and more completely 
harmonized with the rest of our knowledge. Moreover, 
the very molecular theory which we call upon to explain 
the steam-engine involves consequences which, as w T e 
have seen, have been first realized in the radiometer; 
and thus it is that this new instrument, although disap- 
pointing the first expectations of its discoverer, has fur- 
nished a very striking confirmation of this wonderful 
theory. Indeed, the confirmation is so remote and yet 
so close, so unexpected and yet so strong, that the new 
phenomena almost seem to be a direct manifestation of 
the molecular motion which our theory assumes ; and 
when a new discovery thus confirms the accuracy of a 
previous generalization, and gives us additional reason to 
believe that the glimpses we have gained into the order 
of ^Nature are trustworthy, it excites, with reason, among 
scientific scholars the warmest interest. 

And when we consider the vast scope of the molecu- 



MAN'S PLACE IN NATUEE. 125 

lar theory, the order on order of existences which it 
opens to the imagination, how can we fail to be im- 
pressed with the position in which it places man midway 
between the molecular cosmos on the one side and the 
stellar cosmos on the other — a position in which he is 
able, in some measure at least, to study and interpret 
both? 

Since the time to which we referred at the beginning 
of this lecture, when man's dwelling-place was looked 
at as the center of a creation which was solely subser- 
vient to his wants, there has been a. reaction to the oppo- 
site extreme, and we have heard much of the utter insig- 
nificance of the earth in a universe among whose immen- 
sities all human belongings are but as a drop in the 
ocean. "When now, however, we learn from Sir William 
Thomson that the drop of water in our comparison is 
itself a universe, consisting of units so small that, were 
the drop magnified to the size of the earth, these units 
would not exceed in magnitude a cricket-ball,* and 
when, on studying chemistry, we still further learn that 
these units are not single masses but systems of atoms, 
we may leave the illusions of the imagination from the 
one side to correct those from the other, and all will 
teach us the great lesson that man's place in Nature 
is not to be estimated by relations of magnitude, but 

* "Nature," No. 22, March 31, 18*70. 



126 THE RADIOMETER. 

by the intelligence which makes the whole creation his 
own. 

But, if it is man's privilege to follow both the atoms 
and the stars in their courses, he finds that, while thus 
exercising the highest attributes of his nature, he is ever 
in the presence of an immeasurably superior intelli- 
gence, before which he must bow and adore, and thus 
come to him both the assurance and the pledge of a kin- 
ship in which his only real glory can be found. 



MEMOIR OF THOMAS GRAHAM. 

Reprinted from the " Proceedings of the American Academy of Arts 
and Sciences," Vol. VIII, May 21*, 1870. 

It would be difficult to find in the history of science 
a character more simple, more noble, or more symmetri- 
cal in all its parts than that of Thomas Graham, and he 
will always be remembered as one of the most eminent 
of those great students of nature who have rendered our 
Saxon race illustrious. He was born of Scotch parents 
in Glasgow in the year 1805, and in that city, where he 
received his education, all his early life was passed. In 
1837 he went to London as Professor of Chemistry in 
the newly established London University, now called 
University College, and he occupied this chair until the 
year 1855, when he succeeded Sir John Herschel as 
Master of the Royal Mint, a post which he held to the 
close of his life. His death, on the lGth of September 



128 MEMOIR OF THOMAS GRAHAM. 

last (1869), at the age of sixty, was caused by no active 
disease, but was simply the wearing out of a constitution 
enfeebled in youth by privations voluntarily and coura- 
geously encountered that he might devote his life to sci- 
entific study. As with all earnest students, that life was 
uneventful, if judged by ordinary standards; and the 
records of his discoveries form the only materials for his 
biography. 

Although one of the most successful investigators of 
physical science, the late Master of the Mint had not 
that felicity of language or that copiousness of illustra- 
tion which added so much to the popular reputation 
of his distinguished contemporary, Faraday; but his in- 
fluence on the progress of science was not less marked 
or less important. Both of these eminent men were for 
a long period of years best known to the English public 
as teachers of chemistry, but their investigations were 
chiefly limited to physical problems ; yet, although both 
cultivated the border ground between chemistry and 
physics, they followed wholly different lines of research. 
While Faraday was so successfully developing the princi- 
ples of electrical action, Graham with equal success was 
investigating the laws of molecular motion. Each fol- 
lowed with wonderful constancy, as well as skill, a single 
line of study from first to last, and to this concentration 
of power their great discoveries are largely due. 



DIFFUSION OF GASES. 129 

One of the earliest and most important of Graham's 
investigations, and the one which gave the direction to 
his subsequent course of study, was that on the diffusion 
of gases. It had already been recognized that impene- 
trability in its ordinary sense is not, as was formerly 
supposed, a universal quality of matter. Dalton had not 
only recognized that aeriform bodies exhibit a positive 
tendency to mix, or to penetrate through each other, 
even in opposition to the force of gravity, but had made 
this quality of gases the subject of experimental investi- 
gation. He inferred, as the result of his inquiry, " that 
different gases afford no resistance to each other ; but 
that one gas spreads or expands into the space occupied 
by another gas, as it would rush into a vacuum ; at least, 
that the resistance which the particles of one gas offer to 
those of another is of a very imperfect kind, to be com- 
pared to the resistance which stones in the channel of a 
stream oppose to the flow of running water." But, al- 
though this theory of Dalton was essentially correct and 
involved the whole truth, yet it was supported by no 
sufficient evidence, and he failed to perceive the simple 
law which underlies this whole class of phenomena. 

Graham, "on entering on this inquiry, found that 
gases diffuse into the atmosphere with different degrees 
of ease and rapidity." This was first observed by allow- 
ing each gas to diffuse from a bottle into the air through 



130 MEMOIR OF THOMAS GRAHAM. 

a narrow tube in opposition to the solicitation of gravity. 
Afterward an observation of Doebereiner on the escape 
of hydrogen gas by a fissure or crack in a glass receiver 
caused him to vary the conditions of his experiments, 
and led to the invention of the well-known " diffusion 
tube." In this simple apparatus a thin septum of plaster 
of Paris is used to separate the diffusing gases, which, 
while it arrests in a great measure all direct currents 
between the two media, does not interfere with the 
molecular motion. Much later, Graham found in pre- 
pared graphite a material far better adapted to this pur- 
pose than the plaster, and he used septa of this mineral 
to confirm his early results, in answer to certain ill-con- 
sidered criticisms in Bunsen's work on gasometry. These 
septa he was in the habit of calling his " atomic fil- 
ters." 

By means of the diffusion tube, Graham was able to 
measure accurately the relative times of diffusion of 
different gases, and he found that equal volumes of any 
two gases interpenetrate each other in limes which are 
inversely proportional to the square roots of their respec- 
tive densities ; and this fundamental law was the greatest 
discovery of our late foreign associate. It is now uni- 
versally recognized as one of the few great cardinal prin- 
ciples which form the basis of physical science. 

It can be shown, on the principles of pneumatics, 



EFFUSION OF GASES. 131 

that gases should rush into a vacuum with velocities 
corresponding to the numbers which have been found to 
express their diffusion times ; and, in a series of experi- 
ments on what he calls the " effusion " of gases, Graham 
confirmed by trial this deduction of theory. In these ex- 
periments a measured volume of the gas was allowed to 
find its way into the vacuous jar through a minute aper- 
ture in a thin metallic plate, and he carefully distin- 
guished between this class of phenomena and the flowing 
of gases through capillary tubes into a vacuum, in which 
case, however short the tube, the effects of friction ma- 
terially modify the result. This last class of phenomena 
Graham likewise investigated, and designated by the 
term " transpiration." 

"While, however, it thus appears that the results of 
Graham's investigation were in strict accordance with 
Dalton's theory, it must also be evident that Graham was 
the first to observe the exact numerical relation which 
obtains in this class of phenomena, and that all-important 
circumstance entitles him to be regarded as the discoverer 
of the law of diffusion. The law, however, at first enun- 
ciated, was purely empirical, and Graham himself says 
that something more must be assumed than that gases 
are vacua to each other, in order to explain all the phe- 
nomena observed ; and according to his original view 
this representation of the process was only a convenient 



132 MEMOIR OF THOMAS GRAHAM. 

mode of expressing the final result. Such has proved to 
be the case. 

Like other great men, Graham built better than he 
knew. In the progress of physical science during the 
last twenty-five years, two principles have become more 
and more conspicuous, until at last they have completely 
revolutionized the philosophy of chemistry. In the first 
place, it has appeared that a host of chemical as well as of 
physical facts are coordinated by the assumption that all 
substances in the state of gas have the same molecular 
volume, or, in other words, contain the same number of 
molecules in a given space ; and in the second place, it 
has become evident that the phenomena of heat are 
simply the manifestations of molecular motion. Accord- 
ing to this view, the temperature of a body is the vis 
viva of its molecules ; and, since all molecules at a given 
temperature have the same vis viva, it follows that the 
molecules must move with velocities which are inversely 
proportional to the square roots of the molecular weights. 
Moreover, since the molecular volumes are equal, and the 
molecular weights therefore proportional to the densities 
of the aeriform bodies in which the molecules are the 
active units, it also follows that the velocities of the 
molecules in any two gases are inversely proportional to 
the square roots of their respective densities. Thus the 
simple numerical relations first observed in the phe- 



TRANSPIRATION OF GASES. 133 

nomena of diffusion are the direct result of molecular 
motion ; and it is now seen that Graham's empirical law 
is included under the fundamental laws of motion. Thus 
Graham's investigation has become the basis of the new 
science of molecular mechanics, and his measurements 
of the rates of diffusion prove to be the measures of mo- 
lecular velocities. 

From the study of diffusion Graham passed by a nat- 
ural transition to the investigation of a class of phenom- 
ena which, although closely allied to the first as to the 
effects produced, differ wholly in their essential nature. 
Here also he followed in the footsteps of Dalton. This 
distinguished chemist had noticed that a bubble of air 
separated by a film of water from an atmosphere of car- 
bonic anhydride gradually expanded nntil it burst. In 
like manner a moist bladder, half filled with air and tied, 
if suspended in an atmosphere of the same material, be- 
comes in time greatly distended by the insinuation of 
this gas through its substance. This effect can not be 
the result of simple diffusion, for it is to be remembered 
that the thinnest film of water, or of any liquid, is abso- 
lutely impermeable to a gas as such, and, moreover, only 
the carbonic anhydride passes through the film, very lit- 
tle or none of the air escaping outward. The result de- 
pends, first, upon the solution of the carbonic anhydride 
by the water on one surface of the film ; secondly, on 



134 MEMOIR OF THOMAS GRAIIAM. 

the evaporation into the air, from the other surface, of 
the gas thus absorbed. Similar experiments were made 
by Drs. Mitchell and Faust, and others, in which gases 
passed through a film of India-rubber, entering into a 
partial combination with the material on one surface, and 
escaping from it on the other. 

Graham not only considerably extended our knowl- 
edge of this class of phenomena, but also gave us a satis- 
factory explanation of the mode in which these remark- 
able results are produced. He recognized in these cases 
the action of a feeble chemical force, insufficient to pro- 
duce a definite compound, but still capable of determin- 
ing a more or less perfect union, as in the case of simple 
solution. He also distinguished the influence of mass in 
causing the formation or decomposition of such weak 
chemical compounds. The conditions of the phenomena 
under consideration are simply these : 

First. A material for the septum capable of forming 
a feeble chemical union with the gas to be transferred. 

Secondly. An excess of the gas on one side of the film 
and a deficiency on the other. 

Thirdly. Such a temperature that the unstable com- 
pound may form at the surface, where the aeriform con- 
stituent is present in large mass, while it decomposes at 
the opposite surface, where the quantity is less abundant. 

One of the most remarkable results, of Graham's study 



TRANSPIRATION OF HYDROGEN. 135 

of this peculiar mode of transfer of aeriform matter 
through the very substance of solid bodies was an inge- 
nious method of separating the oxygen from the atmos- 
phere. The apparatus consisted simply of a bag of India- 
rubber kept distended by an interior framework, while it 
was exhausted by a Sprengel pump. Under these cir- 
cumstances the selective affinity of the caoutchouc de- 
termines such a difference in the rate of transfer of the 
two constituents of the atmosphere that the amount of 
oxygen in the transpired air rises to forty per cent., and 
by repeating the process nearly pure oxygen may be ob- 
tained. It was at first hoped that this method might 
find a valuable application in the arts, but in this Graham 
was disappointed ; for the same result has since been ef- 
fected by purely chemical methods, which are both cheap- 
er and more rapid. 

These experiments on India-rubber naturally led to 
the study of similar effects produced with metallic septa, 
which, although to some extent previously observed in 
passing gases through heated metallic tubes, had been 
only imperfectly understood. Thus, when a stream of 
hydrogen or carbonic oxide is passed through a red-hot 
iron tube, a no inconsiderable portion of the gas escapes 
through the walls. The same is true to a still greater de- 
gree when hydrogen is passed through a red-hot tube of 
platinum, and Graham showed that, through the walls of 



136 MEMOIR OF THOMAS GRAHAM. 

a tube of palladium, hydrogen gas passes, under the same 
conditions, almost as rapidly as water through a sieve. 
Moreover, our distinguished associate proved that this 
rapid transfer of gas through these dense metallic , septa 
was due, as in the case of the India-rubber, to an actual 
chemical combination of its material with the metal, 
formed at the surface, where the gas is in excess, and as 
rapidly decomposed on the opposite face of the septum. 
He not only recognized as belonging to this class of phe- 
nomena the very great absorption of hydrogen by plati- 
num plate and sponge in the familiar experiment of the 
Doebereiner lamp, but also showed that this gas is a defi- 
nite constituent of meteoric iron — a fact of great interest 
from its bearing on the meteoric theory. 

"We are thus led to Graham's last important discov- 
ery, which was the justification of the theory we have 
been considering, and the crowning of this long line of 
investigation. As may be anticipated from what has 
been said, the most marked example of that order of 
chemical compounds, to which the metallic transpiration 
of aeriform matter we have been considering is due, is 
the compound of palladium with hydrogen. Graham 
showed that, when a plate of this metal is made the neg- 
ative pole in the electrolysis of water, it absorbs nearly 
one thousand times its volume of hydrogen gas— a quan- 
tity approximatively equivalent to one atom of hydrogen 



HYDROGENIUM. 137 

to each atom of palladium. He further showed that the 
metal thus becomes so profoundly altered as to indicate 
that the product of this union is a definite compound. 
Not only is the volume of the metal increased, but its 
tenacity and conducting power for electricity are dimin- 
ished, and it acquires a slight susceptibility to magnet- 
ism, which the pure metal does not possess. The chemi- 
cal qualities of this product are also remarkable. It 
precipitates mercury from a solution of its chloride, and 
in general acts as a strong reducing agent. Exposed to 
the action of chlorine, bromine, or iodine, the hydrogen 
leaves the palladium and enters into direct union with 
these elements. Moreover, although the compound is 
readily decomposed by heat, the gas can not be expelled 
from the metal by simple mechanical means. 

These facts recall the similar relations frequently ob- 
served between the qualities of an alloy and those of the 
constituent metals, and suggest the inference made by 
Graham, that palladium charged with hydrogen is a com- 
pound of the same class — a conclusion which harmonizes 
with the theory long held by many chemists, that hydro- 
gen gas is the vapor of a very volatile metal. This ele- 
ment, however, when combined with palladium, is in a 
peculiarly active state, which sustains somewhat the same 
relation to the familiar gas that ozone bears to ordinary 
oxygen. Hence Graham distinguished this condition of 



138 MEMOIR OF THOMAS GRAHAM. 

hydrogen by the term " hydrogenium." Shortly before 
his death a medal was struck at the Royal Mint from the 
hydrogen palladium alloy in honor of its discovery ; but, 
although this discovery attracted public attention chiefly 
on account of the singular chemical relations of hydro- 
gen, which it brought so prominently to notice, it will be 
remembered in the history of science rather as the beau- 
tiful termination of a life-long investigation, of which the 
medal was the appropriate seal. 

Simultaneously with the experiments on gases, whose 
results we have endeavored to present in the preceding 
pages, Graham carried forward a parallel line of investi- 
gation of an allied class of phenomena, which may be re- 
garded as the manifestations of molecular motion in liquid 
bodies. The phenomena of diffusion reappear in liquids, 
and Graham carefully observed the times in which equal 
weights of various salts dissolved in water diffused from 
an open-mouth bottle into a large volume of pure water, 
in which the bottle was immersed. He was not, how- 
ever, able to correlate the results of these experiments by 
such a simple law as that which obtains with gases. It 
appeared, nevertheless, that the rate of diffusion differs 
very greatly for the different soluble salts, having some 
relation to the chemical composition of the salt which he 
was unable to discover. But he found it possible to di- 
vide the salts into groups of equi-diffusive substances, and 



OSMOSE. 139 

he showed that the rate of diffusion of the several groups 
bear to one another simple numerical ratios. 

More important results were obtained from the study 
of a class of phenomena corresponding to the transpira- 
tion of gases through India-rubber or metallic septa. 
These phenomena, as manifested in the transfer of li- 
quids and of salts in solution through bladder or a similar 
membrane, had previously been frequently studied under 
the names of exosmose and endosmose, but to Graham 
we owe the first satisfactory explanation. As in the 
case of gases, he referred these effects to the influence of 
chemical force, combination taking place on one surface 
of the membrane and the compound breaking up on the 
other, the difference depending, as in the previous in- 
stance, on the influence of mass. He also swept away 
the arbitrary distinctions made by previous experiment- 
ers, showed that this whole class of phenomena are es- 
sentially similar, and called this manifestation of power 
simply " osmose." 

"While studying osmotic action, Graham was led to 
one of his most important generalizations — the recogni- 
tion of the crystalline and amorphous states as funda- 
mental distinctions in chemistry. Bodies in the first 
state he called crystalloids ; those in the last state, colloids 
(resembling glue). That there is a difference in struc- 

ure between crystalloids, like sugar or felspar, and col- 
10 



140 MEMOIR OF THOMAS GRAHAM. 

loids, like barley candy or glass, has of course always 
been evident to the most superficial observer; but 
Graham was the first to recognize in these external differ- 
ences two fundamentally distinct conditions of matter 
not peculiar to certain substances, but underlying all 
chemical differences, and appearing to a greater or less 
degree in every substance. He showed that the power 
of diffusion through liquids depends very much on these 
fundamental differences of condition — sugar, one of the 
least diffusible of the crystalloids, diffusing fourteen times 
more rapidly than caromel, the corresponding colloid. 
He also showed that, in accordance with the general 
chemical rule, while colloids readily combine with crys- 
talloids, bodies in the same condition manifest little or no 
tendency to chemical union. Hence, in osmose, where 
the membranes employed are invariably colloidal, the 
osmotic action is confined almost entirely to crystalloids, 
since they alone are capable of entering into that combi- 
nation with the material of the septum on which the 
whole action depends. 

On the above principles Graham based a simple 
method of separating crystalloids from colloids, which he 
calls " dialysis," and which was a most valuable addition 
to the means of chemical analysis. A shallow tray, pre- 
pared by stretching parchment paper (an insoluble col- 
loid) over a gutta-percha hoop, is the only apparatus re- 



DIALYSIS. 141 

quired. The solution to be "dialyzed" is poured into 
this tray, which is then floated on pure water, whose 
volume should be eight or ten times greater than that of 
the solution. Under these conditions the crystalloids 
will diffuse through the porus septum into the water, 
leaving the colloids on the tray, and in the course of a 
few days a more or less complete separation of the two 
classes of bodies will have taken place. In this way 
arsenious acid and similar crystalloids may be separated 
from the colloidal materials with which, in the case of 
poisoning, they are usually found mixed in the animal 
juices or tissues. 

But, besides having these practical applications, the 
method of dialysis in the hands of Graham yielded the 
most startling results, developing an almost entirely new 
class of bodies, as the colloidal forms of our most familiar 
substances, and justifying the conclusion that the colloidal 
as well as the crystalline condition is an almost universal 
attribute of matter. Thus, he was able to obtain solu- 
tions in water of the colloidal states of aluminic, fevric, 
chromic, stannic, metastannic, titanic, molybdic, tungstic, 
and silicic hydrates, all of which gelatinize under definite 
conditions like a solution of glue. The wonderful nature 
of these facts can be thoroughly appreciated only by 
those familiar with the subject, but all may understand 
the surprise with which the chemist saw such hard, in- 



142 MEMOIR OF THOMAS GRAHAM. 

soluble bodies as flint dissolved abundantly in water and 
converted into soft jellies. These facts are, without doubt, 
the most important contributions of Dr. Graham to pure 
chemistry. 

In this sketch of the scientific career of our late asso- 
ciate, we have followed the logical, rather than the chro- 
nological, order of events, hoping thus to render the re- 
lations of the different parts of his work more intelligible. 
It must be remembered, however, that the two lines of 
investigation we have distinguished were in fact inter- 
woven, and that the beautiful harmony which his com- 
pleted life presents was the result, not of a preconceived 
plan, but of a constant devotion to truth, and a childlike 
faith, which unhesitatingly pressed forward whenever 
nature pointed out the way. 

Although the investigations of the phenomena con- 
nected with the molecular motion in gases and liquids 
were by far the most important of Dr. Graham's labors, 
he also contributed to chemistry many researches which 
can not be included under this head. Of these, which 
we may regard as his detached efforts, the most impor- 
tant was his investigation of the hydrates and other salts 
of phosphorus. It is true that the interpretation he 
gave of the results has been materially modified by the 
modern chemical philosophy, yet the facts which he es- 
tablished form an important part of the basis on which 



WRITINGS. 143 

that philosophy rests. Indeed, it seems as if he almost 
anticipated the later doctrines of types and polybasic 
.acids, and in none of his work did he show more dis- 
criminating observation or acute reasoning. A subse- 
quent investigation on the condition of water in several 
crystalline salts and in the hydrates of sulphuric acid is 
equally remarkable. Lastly, Graham also made interest- 
ing observations on the combination of alcohol with 
salts, on the process of etherification, on the slow oxida- 
tion of phosphorus, and on the spontaneous inflamma- 
bility of phosphureted hydrogen. It would not, how- 
ever, be appropriate in this place to do more than 
enumerate the subjects of these less important studies; 
and we have therefore only aimed in this sketch to give 
a general view of the character of the field which this 
eminent student of nature chiefly cultivated, and to show 
how abundant was the harvest of truth which we owe to 
his faithful toil. 

Graham was not a voluminous writer. His scientific 
papers were all very brief, but comprehensive, and his 
" Elements of Chemistry " was his only large work. 
This was an admirable exposition of chemical physics, 
as well as of pure chemistry, and gave a more philosophi- 
cal account of the theory of the galvanic battery than 
had previously appeared. Our late associate was fortu- 
nate in receiving during life a generous recognition of 



144 MEMOIR OF THOMAS GRAIIAM. 

the value of his labors. His membership was sought by 
almost all the chief scientific societies of the world, and 
he enjoyed to a high degree the confidence and esteem 
of his associates. Indeed, he was singularly elevated 
above the petty jealousies and belittling quarrels which 
so often mar the beauty of a student's life, while the 
great loveliness and kindliness of his nature closely en- 
deared him to his friends. 

In concluding, we must not forget to mention that 
most genial trait of Graham's character, his sympathy 
with young men, which gave him great influence as a 
teacher in the college with which he was long associated. 
There are many now prominent in the scientific world 
who have found in his encouragement the strongest in- 
centive to perseverance, and in his approval and friend- 
ship the best reward of success. 



VI. 

MEMOIR OF WILLIAM HALLOWES 
MILLER. 

Reprinted from the " Proceedings of the American Academy of Arts 
and Sciences," Vol. XVI, May 2^, 1881. 

William TTallqwes Millek, who was elected For- 
eign Honorary Member of this Academy in the place of 
C. F. Naumann, May 26, 1874, died at his residence in 
Cambridge, England, on the 20th of May, 1880, at the 
age of seventy-nine, having been born at Yelindre, in 
Wales, April 5, 1801. His life was singularly unevent- 
ful, even for a scholar. Graduating with mathematical 
honors at Cambridge in 1826, he became a fellow of his 
college (St. John's) in 1829, and was elected Professor 
of Mineralogy in the University in 1832. Under the in- 
fluence of the calm and elegant associations of this ancient 
English university, Miller passed a long and tranquil life 
— crowded with useful labors, honored by the respect and 



146 MEMOIR OF WILLIAM HALLOWES MILLER. 

love of his associates, and blessed by congenial family 
ties. This quiet student-life was exactly suited to his 
nature, which shunned the bustle and unrest of our 
modern world. For relaxation, even, he loved to seek the 
retired valleys of the Eastern Alps ; and the description 
which he once gave to the writer, of himself sitting at 
the side of his wife amid the grand scenery, intent on 
developing crystallographic formulae, while the accom- 
plished artist traced the magnificent outlines of the Dolo 
mite mountains, was a beautiful idyl of science. 

Miller's activities, however, were not confined to the 
University. In 1838 he became a Fellow of the Royal 
Society, and in 1856 he was appointed its Foreign Secre- 
tary — a post for which he was eminently fitted, and which 
he filled for many years. In 1843 he was selected one 
of a committee to superintend the construction of the 
new Parliamentary standards of length and weight, to 
replace those which had been lost in the fire which con- 
sumed the Houses of Parliament in 1834, and to Pro- 
fessor Miller was confided the construction of the new 
standard of weight. His work on this important com- 
mittee, described in an extended paper published in the 
"Philosophical Transactions " for 1856, was a model of 
conscientious investigation and scientific accuracy. Pro- 
fessor Miller was subsequently a member of a new Royal 
Commission for " examining into and reporting on the 



PUBLIC SERVICES. 147 

state of the secondary standards, and for considering 
every question which could affect the primary, secondary, 
and local standards " ; and in 1870 he was appointed a 
member of the " Commission Internationale du Metre." 
His services on this commission were of great value, and 
it has been said that " there was no member whose opin- 
ions had greater weight in influencing a decision upon 
any intricate and delicate question." 

Valuable, however, as were Professor Miller's public 
services on these various commissions, his chief work was 
at the University. His teacher, Dr. William "Whewell — 
afterward the Master of Trinity College — was his imme- 
diate predecessor in the Professorship of Mineralogy at 
Cambridge. This great scholar, whose encyclopaedic 
mind could not long be confined in so narrow a field, 
held the professorship only four years ; but during this 
period he devoted himself with his usual enthusiasm to 
the study of crystallography, and he accomplished a most 
important work in attracting to the same study young 
Miller, who brought his mathematical training to its elu- 
cidation. It was the privilege of Professor Miller to 
accomplish a unique work, for the like of which a more 
advanced science, with its multiplicity of details, will 
offer few opportunities. 

The foundations of crystallography had been laid long 
before Miller's time. Haiiy is usually regarded as the 



148 MEMOIR OF WILLIAM HALLOWES MILLER. 

founder of the science; for he first discovered the im- 
portance of cleavage, and classed the known facts under 
a definite system. Taking cleavage as his guide, and 
assuming that the forms of cleavage were not only the 
primitive forms of crystals as a whole, but also the forms 
of their integrant molecules, he endeavored to show that 
all secondary forms might be derived from a few primary 
forms, regarded as elements of nature, by means of de- 
crements of molecules at their edges. In like manner 
he showed that all the forms of a given mineral, like 
fluor-spar or calcite, might be built up from the integrant 
molecules by skillfully placing together the primitive 
forms. Haiiy's dissection of crystals, in a manner which 
appeared to lead to their ultimate crystalline elements, 
gained for his system great popular attention and ap- 
plause. The system was developed with great perspicuity 
and completeness in a work remarkable for the vivacity 
of its style and the felicity of its illustration. Moreover, 
a simple mathematical expression was given to the sys- 
tem, and the notation which Haiiy invented to express the 
relation of the secondary to the primary forms, as modi- 
fied and improved by Levy, is still used by the French 
mineralogists. 

The system of Haiiy, however, was highly artificial, 
and only prepared the way for a simpler and more gen- 
eral expression of the facts. The German crystallogra- 



FUNDAMENTAL LAW. 149 

pher, Weiss, seems to be the first to have recognized the 
truth that the decrements of Haiiy were merely a me- 
chanical mode of representing the fact that all the sec- 
ondary faces of a crystal make intercepts on the edges of 
the primitive form which are simple multiples of each 
other ; and, this general conception once gained, it was 
soon seen that these ratios could be as simply measured 
on the axes of symmetry of the crystal as on the edges 
of the fundamental forms ; and, moreover, that, when 
crystal forms are viewed in their relation to these axes, a 
more general law becomes evident, and the artificial dis- 
tinction between primary and secondary forms disappears. 
Thus became slowly evolved the conception of a 
crystal as a group of similar planes symmetrically dis- 
posed around certain definite and obvious systems of 
axes, and so placed that the intercepts, or parameters, on 
these axes bore to each other a simple numerical ratio. 
Representing by a : h : e the ratio of the intercepts of a 
plane on the three axes of a crystal of a given substance, 
then the intercepts of every other plane of this, or of any 
other crystal of the same substance, conform to the gen- 
eral proportion m a : n b : p c, in which m, n, p are three 
simple whole numbers. This simple notation, devised 
by Weiss, expressed the fundamental law of crystal- 
lography; and the conception of a crystal as a system 
of planes, symmetrically distributed according to this law, 



150 MEMOIR OF WILLIAM HALLOWES MILLER. 

was a great advance beyond the decrements of Haiiy, an 
advance not unlike that of astronomy from the system of 
vortices to the law of gravitation. Yet, as the mechan- 
ism of vortices was a natural prelude to the law of New- 
ton, so the decrements of Haiiy prepared the way for the 
wider views of the German crystallographers. 

Whether Weiss or Mohs contributed most to advance 
crystallography to its more philosophical stage, it is not 
important here to inquire. Each of these eminent schol- 
ars did an important work in developing and diffusing 
the larger ideas, and in showing by their investigations 
that the facts of nature corresponded to the new concep- 
tions. But to Carl Friedrich Naumann, Professor at the 
time in the " Bergakademie zu Freiberg," belongs the 
merit of first developing a complete system of theoreti- 
cal crystallography based on the laws of symmetry and 
axial ratios. His " Lehrbuch der reinen und angewandt- 
en Krystallographie," published in two volumes at Leip- 
zig in 1830, was a remarkable production, and seemed to 
grasp the whole theory of the external forms of crystals. 
Nauinann used the obvious and direct methods of ana- 
lytical geometry to express the quantitative relations be- 
tween the parts of a crystal ; and, although his methods 
are often unnecessarily prolix and his notation awkward, 
his formulae are well adapted to calculation, and easily in- 
telligible to persons moderately disciplined in mathematics. 



TRACT ON CRYSTALLOGRAPHY. 151 

But, however comprehensive and perfect in its de- 
tails, the system of Naumann was cumbrous, and lacked 
elegance of mathematical form. This arose chiefly from 
the fact that the old methods of analytical geometry 
were unsuited to the problems of crystallography ; but it 
resulted also from a habit of the German mind to dwell 
on details and give importance to systems of classifica- 
tion. To Naumann the six crystalline systems were as 
much realities of nature as were the forms of the inte- 
grant molecules to Haiiy, and he failed to grasp the larger 
thought which includes all partial systems in one com- 
prehensive plan. 

Our late colleague, Professor Miller, on the other 
hand, had that power of mathematical generalization 
which enabled him to properly subordinate the parts to 
the whole, and to develop a system of mathematical crys- 
tallography of such simplicity and beauty of form that it 
leaves little to be desired. This was the great work of 
his life, and a work worthy of the university which had 
produced the "Principia." It was published in 1839, 
under the title, "A Treatise on Crystallography"; and 
in 1863 the substance of the work was reproduced in a 
more perfect form, still more condensed and generalized, 
in a thin volume of only eighty-six pages, which the au- 
thor modestly called, " A Tract on Crystallography." 

Miller began his study of crystallography with the 



152 MEMOIR OF WILLIAM HALLO WES MILLER. 

same materials as Naumann ; but, in addition, lie adopt- 
ed the beautiful method of Franz Ernst Neumann of re- 
ferring the faces of a crystal to the surface of a circum- 
scribed sphere by means of radii drawn perpendicular to 
the faces. The points where the radii meet the spheri- 
cal surface are the poles of the faces, and the arcs of 
great circles connecting these poles may obviously be 
used as a measure of the angles between the crystal faces. 
This invention of Neumann's was the germ of Miller's 
system of crystallography, for it enabled the English 
mathematician to apply the elegant and compendious 
methods of spherical trigonometry to the solution of 
crystallographic problems; and Professor Miller always 
expressed his great indebtedness to Neumann, not only 
for this simple mode of denning the position of the faces 
of a crystal, but also for his method of representing the 
relative position of the poles of the faces on a plane sur- 
face by a beautiful application of the methods of stereo- 
graphic and gnomonic projection. This method of rep- 
resenting a crystal shows very clearly the relations of the 
parts, and was undoubtedly of great aid to Miller in as- 
sisting him to generalize his deductions. 

From the outset, Professor Miller apprehended more 
clearly than any previous writer the all-embracing scope 
of the great law of crystallography. He opens his treat- 
ise with its enunciation, and, from this law as the f unda- 



INDICES. 153 

mental principle of the subject, the whole of his system 
of crystallography is logically developed. Beyond this, 
all that is peculiar to Miller's system is involved in two 
or three general theorems. The rest of his treatise con- 
sists of deductions from these principles and their appli- 
cation to particular cases. 

One of the most important of these principles, and 
one which in the treatise is involved in the enunciation 
of the fundamental law of crystallography, is in its 
essence nothing but an analytical device. As we have 
already stated, "Weiss had shown that, if a : b : c represent 
the ratio of the intercepts of any plane of a crystal on 
the three axes a?, y, and z, respectively, the intercepts of 
any other possible plane must satisfy the proportion — 

A: B: C= ma : nb :pc, 

in which m, n, and^> are simple whole numbers. The 
irrational values a, b, and c are fundamental magnitudes 
for every crystalline substance ; * and Miller called these 
relative magnitudes the parameters of the crystals, while 
he called the whole numbers, m, n, and p, the indices of 
the respective planes. But, instead of writing the pro- 

* For example, the native crystals of sulphur have a : b : c = 1 : 2*340 : 1*233. 
Crystals of gypsum have a : b : c = 1 : 0*413 : 0*691. 

Crystals of tin-stone have a : h : c = 1 : 1 : 0*6724. ( 

And crystals of common salt have a : 6 : c = 1 : 1:1. 



154 MEMOIR OF WILLIAM HALLOWES MILLER. 

portion which expresses the law of crystallography as 
above, he gave to it a slightly different form, thus : 

h Tc I ' 
and used in his system for the indices of a plane the 
values h:7c:l, which are also in the ratio of whole num- 
bers, and usually of simpler whole numbers than m : n :p. 
This seems a small difference ; for h Tc I in the last pro- 
portion are obviously the reciprocals of m np in the first ; 
but the difference, small as it is, causes a wonderful sim- 
plification of the formulae which express the relations be- 
tween the. parts of a crystal. From the last proportion we 
derive at once - 

1_ a _ 1_ m h ' _ • l_ c 

h ' A~ Tc ' B~ I J 

which is the form in which Miller stated his fundamental 
law. 

If P represents the " pole " of a face whose " indices " 
are h lc Z, that is, represents the point where the radius 
drawn normal to the face meets the surface of the sphere 
circumscribed around the crystal (the sphere of projec- 
tion, as it is called), and if X, Y, Z represent the points 
where the axes of the crystal meet the same spherical 
surface,* then it is evident that X JT, XZ, and JTZ are 

* The origin of the axes is always taken as the center of the sphere of 
projection. 



THE ZONE EQUATION. 155 

the arcs of great circles, which measure the inclination of 
the axes to each other, and that PJ, PY, and P Z are 
arcs of other great circles, which measure the inclination 
of the plane (A Jc V) on planes normal to the respective axes ; 
and, also, that these several arcs form the sides of spheri- 
cal triangles thus drawn on the sphere of projection. 
ISow, it is very easily shown that 

-cos PX= h -cosPY = G -cosPZ; 

h Jc I 

and by means of this theorem we are able to reduce a 
great many problems of crystallography to the solution of 
spherical triangles. 

Another very large class of problems in crystallogra- 
phy is based on the relation of faces in a zone ; that is, of 
faces which are all parallel to one line called the zone 
axis, and whose mutual intersections, therefore, are all 
parallel to each other. If, now, h Jc I and p q r are the 
indices of any two planes of a zone (not parallel to each 
other), any other plane in the same zone must fulfill the 
condition expressed by the simple equation 

where u v and w are the indices of the third plane, and 
u v w have the values 

u = Jcr-lq v = lp-hr w = hq- hp. 



156 MEMOIR OF WILLIAM IIALLOWES MILLER. 

» 
Since hkl smdpqr are whole numbers, it is evident that 

uvw must also be whole numbers, and these quantities 
are called the indices of the zone. The three whole num- 
bers which are the indices of a plane when written in suc- 
cession serve as a very convenient symbol of that plane, 
and represent to the crystallographer all its relations; 
and in like manner Miller used the indices of a zone in- 
closed in brackets as the symbol of that zone. Thus 123, 
531, 010 are symbols of planes, and [111], [213], [001] 
symbols of zones. 

An additional theorem enables us to calculate the 
symbols of a fourth plane in a zone when the angular 
distances between the four planes and the symbols of 
three of them are known, but this problem can not be 
made intelligible with a few words. 

The few propositions to which we have referred in- 
volve all that is essential and peculiar to the system of 
Professor Miller. These given, and the rest could be at 
once developed by any scholar who was familiar with the 
facts of crystallography ; and the circumstance that its 
essential features can be so briefly stated is sufficient to 
show how exceedingly simple the system is. At the same 
time, it is wonderfully comprehensive, and the student 
who has mastered it feels that it presents to him in one 
grand view the entire scheme of crystal forms, and that 
it greatly helps him to comprehend the scheme as a whole, 



MATERIAL CONCEPTIONS. 157 

and not simply as the sum of certain distinct parts. So 
felt Professor Miller himself ; and, while he regarded the 
six systems of crystals of the German crystallographers 
as natural divisions of the field, he considered that they 
were bounded by artificial lines which have no deeper 
significance than the boundary lines on a map. How 
great the unfolding of the science from Haiiy to Miller, 
and yet now we can see the great fundamental ideas shin- 
ing through the obscurity from the first ! What we now 
call the parameters of a crystal were to Haiiy the funda- 
mental dimensions of his " integrant molecules," our in- 
dices were his " decrements," and our conceptions of sym- 
metry his " fundamental forms." There has been nothing 
peculiar, however, in the growth of crystallography. This 
growth has followed the usual order of science, and here 
as elsewhere the early, gross, material conceptions have 
been the stepping-stones by which men rose to higher 
things. In sciences like chemistry, which are obviously 
still in the earlier stages of their development, it would 
be well if students would bear in mind this truth of his- 
tory, and not attach undue importance to structural for- 
mulae and similar mechanical devices, which, although 
useful for aiding the memory, are simply hindrances to 
progress as soon as the necessity of such assistance is 
passed. And, when the life of a great master of science 
has ended, it is well to look back over the road he has 



158 MEMOIR OF WILLIAM HALLO WES MILLER. 

traveled, and, while we take courage in his success, con- 
sider well the lesson which his experience has to teach ; 
and, as progress in this world's knowledge has ever been 
from the gross to the spiritual, may we not rejoice as those 
who have a great hope ? 

Although the exceeding merit of the " Treatise on 
Crystallography " casts into the shade all that was subor- 
dinate, we must not omit to mention that Professor Mil- 
ler published an early work on hydrostatics, and numer- 
ous shorter papers on mineralogy and physics, which 
were all valuable, and constantly contained important ad- 
ditions to knowledge. Moreover, the " New Edition of 
Phillips's Mineralogy," which he published in 1852 in 
connection with H. J. Brooke, owed its chief value to a 
mass of crystallographic observations which he had made 
with his usual accuracy and patience during many years, 
and there tabulated in his concise manner. As has been 
said by one of his associates in the Poyal Society, " it is 
a monument to Miller's name, although he almost ex- 
punged that name from it." * It is due to Professor 
Miller's memory that his works should be collated, and 
especially that by a suitable commentary his " Tract on 
Crystallography " should be made accessible to the great 

* " Obituary Notices from the Proceedings of the Royal Society," No. 
20&, 1880, to which the writer has been indebted for several biographical 
details. 



CHARACTERISTICS OF MIND. 159 

body of the students of physical science, who have not, 
as a rule, the ability or training which enables them to 
apprehend a generalization when solely expressed in math- 
ematical terms. The very merits of Professor Miller's 
book as a scientific work render it very difficult to the 
average student, although it only involves the simplest 
forms of algebra and trigonometry. 

Independence, breadth, accuracy, simplicity, humility, 
courtesy, are luminous words which express the character 
of Professor Miller. In his genial presence the young 
student felt encouraged to express his immature thoughts, 
which were sure to be treated with consideration, while 
from a wealth of knowledge the great master made the 
error evident by making the truth resplendent. It was 
the greatest satisfaction to the inexperienced investigator 
when his observations had been confirmed by Professor 
Miller, and he was never made to feel discouraged when 
his mistakes were corrected. The writer of this notice 
regards it as one of the great privileges of his youth, a'nd 
one of the most important elements of his education, to 
have been the recipient of the courtesies and counsel of 
three great English men of science, who have always been 
" his own ideal knights," and these noble knights were 
Faraday, Graham, and Miller. 



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